UNIVERSITY  OF  CALIFORNIA 
AT   LOS  ANGELES 


HELD  -™  Orncc  METHODS 


STUDENTS   IN   SURVEYING. 


BY 


W1LLIA/V\  D.   PENCE, 

Professor    of     Civil     Engineering. 
Purdue  University. 


A\ILO  S.   KETCMUAV 

Assistant  Professor  of  Civil  Engineering 
University  of  Illinois. 


PUBLISHED    BY   THf:    AUTHORS. 


Copyright.  1900. 


WILLIAM  D.  PKNCK 

AND 

MILO  S.  KKTCHUM; 


TA 

55  \ 


TABLE  OF  CONTENTS. 


Page 
CHAPTER  I.  -GENERAL  INSTRUCTIONS  1 

CHAPTER  II.— THE  CHAIN  AND  TAPE.  13 

Problem  A  1.  Length  of  Pace 24 

A  2.  Distances  by  Pacing 24 

A  3.  Axeman  and  Flagman  Practice 26 

A  4.  Range  Pole  Practice , 26 

A  5.  Standardizing  Chain  or  Tape 26 

A  6.  Distances  with  Surveyors'  Chain 27 

A  7.  Distances  with  Engineers'  Chain 28 

A  8.  Distances  with  100-foot  Steel  Tape 28 

A  9.  Horizontal  Distance  on  Slope 30 

A10.  Angles  of  Triangle  with  Tape 32 

All.  Survey  of  Field  with  Tape 32 

A12.  Area  by  Perpendicular  Method 32 

A13.  Area  by  Three-Side  Method 34 

A14.  Area  by  Angle  Method 34 

A15.  Area  from  Plat 34 

A16.  Survey  of  Field  with  Curved  Boundary 38 

A17.  Area  of  Field  with  Curved  Boundary 36 

A18.  Area  (of  same)  from  Plat 38 

A19.  Passing  an  Obstacle  with  Tape 38 

A20.  Obstructed  Distance  with  Tape 40 

A21.  Running  in  Curve  with  Tape 40 

A22.  Discussion  of  Errors  of  Chaining 42 

A23.  Testing  Standard  of  Length 42 

A24.  Constants  of  Steel  Tape 44 

A25.  Comparison  of  Chains  and  Tapes 44 


TABLE  OF  CONTENTS. 

Pas?e 
CHAPTER  III.— THE  COMPASS.  45 

Problem  B  1.  Declination  of  Needle 51 

B  2.  Angles  of  Triangle  with  Compass 52 

B  3.  Traverse  of  Field  with  Compass 54 

B  4.  Area  of  Field  with  Compass 51 

B  5.  Adjustment  of  Compass 56 

B  6.  Comparison  of  Compasses . .  56 


CHAPTER  IV.— THE  LEVEL.  57 

Problem  C  1.  Differential  Leveling  with  Hand  Level 76 

C  2.  Differential  Leveling,   Engine ars'   Level...  78 

C  3.  Profile  Leveling  for  Drain 78 

C  4.  Railroad    Profile    Leveling 82 

C  5.  Vertical  Curve  83 

C  6.  Establishing  Grade  Line 84 

C  7.  Survey  of  Line  Shafting 84 

C  8.  Contour  Leveling 87 

C  9.  Use   of  Contour   Map 89 

CIO.  Delicacy  of  Bubble  Vial 89 

Cll.  Comparison  of  Level  Telescopes 90 

C12.  Tests  of  Wye  Level 90 

C13.  Adjustment  of  Wye  Level 91 

C14.  Sketching  Wye  Level 92 

CIS.  Tests  of  Dumpy  Level 92 

C16.  Adjustment  of  Dumpy  Level 92 

C17.  Sketching  Dumpy  Level 92 

C18.  Stretching  Cross-Hairs 93 

C19.  Error  of  Setting  Level  Target 03 

C20.  Comparison  of  Engineers'  Levels 94 


TABLE  OF  CONTENTS. 

Page 
CHAPTER  V.— THE  TRANSIT.  95 

Problem  D  1.  Angles   of   Triangle   with   Transit 10- 

D  2.  Prolongation  of  Line  with  Transit 104 

D  3.  Intersection  of  Two  Lines  with  Transit. .  .10'i 

D  4.  Triangulation  Across  River 106 

D  5.  Passing  Obstacle  with  Transit 106 

D  6.  Traverse  of  Field  with  Transit 108 

D  7.  Area  of  Field  with  Transit 108 

D  8.  Staking  Out  Building 110 

D  9.  Height  of  Tower  with  Transit 110 

D10.  Angles  of  Triangle  by  Repetition 1.12 

Dll.  True  Meridian  by  Polaris  at  Elongation.  .111 
D12.  True  Meridian  by  Polaris  at  Any  Time.    .  .115 

D13.  Comparison  of  Transit  Telescopes     118 

D14.  Test  of  Transit 118 

D15.  Adjustment   of  Transit 118 

D16.  Sketching   Transit L19 

D17.  Error  of   Setting  Flag  Pole 120 

D18.  Comparison  of  Engineers'  Transits 120 


CHAPTER  VI.— TOPOGRAPHIC  SURVEYING.  121 

Problem  E  1.  Stadia  Constants.,   with   Fixed  Hairs 132 

E  2.  Stadia    Reduction   Table 134 

E  3.  Azimuth  Traverse  with  Stadia 134 

E  4.  Plane  Table  Survey  by  Radiation 135 

E  5.  Plane  Table  Survey  by  Traversing 135 

E  6.  Plane  Table  Survey  by  Intersection 136 

E  7.  Three  Point  Problem  with  Plane  Table...  136 

E  8.  Angles  of  Triangle  with  Sextant 13*i 

E  9.  Coefficients  of  Standard  Taps 139 

E10.  Measurement  of  Base  Line...  ...139 


TABLE  OF  CONTENTS. 

Page 
Ell.  Calculation  of  Triangulation  System     ....  139 

E12.  Sketching   Topography 140 

E13.  Topography  with  Transit  and  Stadia 140 

E14.  Topography  with  Plane  Table  and  Stadia . .  142 

E15.  Topographic   Survey 143 

E16.  Survey  for  Street  Improvements 143 


CHAPTER  VII.— LAND  SURVEYING.  145 

Problem  F  1.  Investigation  of  Land  Corner 157 

F  2.  Perpetuation  of  Land  Corner 158 

F  3.  Reestablishing  Quarter-Section  Corner 159 

F  4.  Reestablishing  Section  Corner ISO 

F  5.  Resurvey  of  Section 160 

F  6.  Resurvey  of  City  Block 163 

F  7.  Resurvey  by  Metes  and  Bounds 163 

F  8.  Partition  of  Land .164 

F  9.  Design  and  Survey  of  Town  Site 1M 


CHAPTER  VIII.— RAILROAD   SURVEYING         167 

Problem  G  1.  Review  of  Instrumental  Adjustments 196 

G  2.  Use  of  Field  Equipment 196 

G  3.  Preliminary  Field  Curve  Practice 197 

G  4.  Indoor  Curve  Problems 198 

CHAPTER  IX.— ERRORS  OF  SURVEYING.  199 
CHAPTER  X.— METHODS  OF  COMPUTING  211 
CHAPTER  XL— FREE  HAND  LETTERING  225 


PREFACE. 


In  preparing  this  manual  the  following  points  have  been 
kept  especially  in  view:  (1)  To  provide  a  simple  and  com- 
prehensive text  designed  to  anticipate  and  supplement, 
rather  than  replace,  the  usual  elaborate  treatise.  (2)  To 
bring  the  student  into  immediate  familiarity  with  approved 
surveying  methods.  (3)  To  cultivate  the  student's  skill  in 
the  rare  arts  of  keeping  good  field  notes  and  making  reliable 
calculations. 

It  is  believed  that  the  discussions  of  the  different  instru- 
ments, their  use  and  theory,  at  the  beginning  of  the  several 
chapters  is  unusually  simple,  especially  in  the  relations  of 
the  elementary  lines. 

The  several  series  of  practice  problems  at  the  conclusion 
of  the  respective  chapters  are  arranged  so  as  to  give  the 
student  familiarity  with  the  use  of  the  instrument  before 
taking  up  its  theory  and  adjustments,  this  ord>er  bein^r  more 
effective  than  the  reverse.  The  interest  of  the  student  may 
be  stimulated  and  'his  gain  in  skill  promoted  by  giving  him 
practice  with  level  and  transit  very  early  in  the  course, 
after  which  the  scope  of  the  work  may  be  much  more  flex- 
ible both  for  student  and  instructor. 

Since  the  list  of  problems  is  more  extended  than  can  be 
covered  in  the  time  usually  available  for  surveying  field 
practice,  some  range  is  permitted  in  the  choice  of  work  from 
year  to  year  and  under  varying  local  conditions.  By  using 
some  discrimination  in  selecting  the  more  important  prob- 
lems for  actual  field  work,  the  others  may  be  covered  suf- 
ficiently by  class  room  discussions. 

The  consistent  treatment  of  errors  of  surveying  receives 
attention  throughout  the  book.  The  methods  of  work  both 
in  field  and  office  are  designed  both  to  reveal  and.  as  far 
as  possible,  to  eliminate  blunders  and  errors,  and  the  tests 
of  precision  are  borrowed  from  the  most  rational  current 
practice.  The  distribution  of  residual  errors  falling  within 
the  permissible  limits  likewise  receives  due  consideration. 

An  important  innovation  in  this  manual  is  the  liberal 
use  of  field  note  and  other  forms  executed  according  to  the 
standard  required  of  the  student  in  like  work.  The  nigh 


PREFACE. 

value  of  such  samples  in  developing  the  student's  skill  in 
this  important  detail  of  field  work  has  been  well  estab- 
lished. It  will  be  seen  that  the  forms  are  prescribed  in 
liberal  number  in  the  earlier  stages  of  the  work  while  the 
student  is  engaged  in  fixing  a  standard  of  quality,  but  that 
farther  on  he  is  required  more  and  more  to  devise  his  own 
forms.  A  valuable  feature  of  this  system  is  the  liberal 
amount  of  practice  obtained  in  freehand  lettering  and  tl-e 
marked  effect  on  the  drafting  and  other  kinds  of  work. 

It  is  suggested  that  the  student  should  be  trained  to  be 
self-reliant  by  requiring  him  to  verify  his  own  results  be- 
fore submitting  them  for  criticism.  Likewise  he  should  be 
encouraged  to  be  genuine  by  placing  him  on  his  honor. 

This  somewhat  informal  guide  to  field  and  office  methods 
is  issued  primarily  for  the  use  of  the  authors'  classes,  but 
it  is  hoped  that  others  ?s  well  may  find  it  of  value  in  pre- 
senting principles  to  the  beginner,  and  in  cultivating  his 
spirit  and  manual  skill. 

December,  1900  W.  D.  P. 

M.  S.  K. 


SPECIFICATIONS  FOR  A  GOOD  ENGINEER. 

"A  good  engineer  must  be  of  inflexible  integrity,  sober, 
truthful,  accurate,  resolute,  discreet,  of  cool  and  sound 
judgment,  must  have  command  of  his  temper,  must  have 
courage  to  resist  and  repel  attempts  at  intimidation,  a  firm- 
ness that  is  proof  against  solicitation,  flattery  or  improper 
bias  of  any  kind,  must  take  an  interest  in  his  work,  must 
be  energetic,  quick  to  decide,  prompt  to  act,  must  be  fair 
and  impartial  as  a  judge  on  the  bench,  must  have  experi- 
ence in  his  work  ami  in  dealing  with  men,  which  implies 
s-cme  maturity  of  years,  must  have  business  habits  and 
knowledge  of  accounts.  Men  who  combine  these  qualities 
are  not  to  be  picked  up  every  day.  Still  they  can  be  found. 
But  they  are  greatly  in  demand,  and  when  found,  they  are 
worth  their  price;  rather  they  are  beyond  price,  and  their 
value  can  not  be  estimated  by  dollars."— CJ> iff 
$t(irli)>y's  Report  to  tJi<>  .)//.v.s-/.v.s- //>/</  fierce 


CHAPTER  I. 
GENERAL  INSTRUCTIONS. 


FIELD  WORK. 

Habitual  Correctness. — Habitual  correctness  is  a  duty. 
Error  should  be  looked  upon  as  i>nib<il>h\  and  every  precau- 
tion-taken to  verify  data  and  results.  Unchecked  work  may 
always  be  regarded  as  doubtful.  A  discrepancy  which  is 
found  by  the  maker  in  time  to  be  corrected  by  him  before 
any  damage  is  done  is  not  necessarily  discreditable,  pro- 
vided the  error  is  not  repeated.  However,  Jmhitiuil  error 
is  not  only  discreditable  but  dishonorable  as  well,  and  noth- 
ing except  intentional  dishonesty  injures  the  reputation  of 
the  engineer  more  quickly  or  permanently. 

Consistent  Accuracy.— The  degree  of  precision  sought 
in  the  field  measurements  should  be  governed  strictly  by  the 
dictates  of  common  sense  and  experience.  Due  considera- 
tion of  the  purposes  of  the  survey  and  of  the  time  available 
will  enable  one  to  avoid  extreme  precision  when  ordinary 
care  would  suffice,  or  crudeness  when  exactness  is  required, 
or  inconsistency  between  the  degrees  of  precision  observed 
in  the  several  parts  of  the  survey.  It  is  a  very  common 
practice  of  beginners,  and  of  many  experienced  engineers 
as  well,  to  carry  calculated  results  far  beyond  the  consistent 
exactness. 

Speed.— Cultivate  the  habit  of  doing  the  field  work 
quickly  as  well  as  accurately.  True  skill  involves  both 
quantity  and  quality  of  results.  However,  v/hile  the  habit 
of  rapid  work  can  and  should  be  acquired,  the  speed  at- 
tempted in  any  given  problem  should  never  be  such  as  to 
cast  doubt  upon  the  results.  Slowness  due  to  laziness  is 
intolerable. 

Familiarity  with  Instructions.— The  instructions     for 


2  GENERAL  INSTRUCTIONS. 

the  day's  work  should  be  read  over  carefully,  and  prelim- 
inary steps,  such  as  the  preparation  of  field  note  forms, 
should  be  taken  so  as  to  save  time  and  make  the  work  in 
the  field  as  effective  as  possible.  The  ability  and  also  the 
desire  to  understand  and  obey  instructions  are  as  essential 
as  the  skill  to  execute  them. 

Inferior  Instruments. — Should  a  poor  instrument  or 
other  equipment  be  assigned,  a  special  effort  should  be  made 
to  secure  excellent  results.  In  actual  practice,  beginners 
often  have  to  work  with  defective  instruments,  but  they 
should  never  seek,  nor  are  they  permitted,  to  justify  poor 
results  by  the  character  of  the  field  equipment.  The  stu- 
dent should  therefore  welcome  an  occasional  opportunity  to 
secure  practice  with  poor  instruments. 

Alternation  of  Duties. — The  members  of  each  party 
should  alternate  in  discharging  the  several  kinds  of  service 
involved  in  the  field  problems,  unless  otherwise  instructed. 
Training  in  the  subordinate  positions  is  essential  whether 
the  beginner  is  to  occupy  them  in  actual  practice  or  not, 
for  intelligent  direction  of  work  demands  thorough  knowl- 
edge of  all  its  details. 

Field  Practice  Decorum. — The  decorum  of  surveying 
field  practice  should  conform  reasonably  to  that  observed 
in  other  laboratory  work. 


THE  CARE  OF  FIELD  EQUIPMENT. 

Responsibility.— The  student  is  responsible  for  the  prop- 
er use  and  safe  return  of  all  equipment.  All  cases  of 
breakage,  damage,  loss  or  misplacement  must  be  reported 
promptly.  The  equipment  should  be  examined  when  as- 
signed and  an  immediate  report  made  of  any  injury  or  de- 
ficiency, so  that  responsibility  may  be  properly  fixed. 

PRECAUTIONS.— Careful  attention  to  the  following 
practical  suggestions  will  save  needless  wear  to  the  equip- 
ment and  reduce  the  danger  of  accidents  to  a  minimum, 
besides  adding  to  the  quality  and  speed  of  the  work. 

Tripod.— Inspect  the  tripod  legs  and  shoes.  The  leg  is 
of  the  proper  tightness,  if  when  lifted  to  an  elevated  posi- 


FIELD  EQUIPMENT.  3 

tion  it  sinks  gradually  of  its  own  weight.    The  tripod  shoes 
should  be  tight  and  have  reasonably  sharp  points. 

Setting  Up  Indoors. — In  setting  up  the  instrument  in- 
doors press  the  tripod  shoes  firmly  into  the  floor,  prefer- 
ably with  each  point  in  a  crack.  Avoid  disturbing  other 
instruments  in  the  room. 

Instrument  Case.— Handle  the  instrument  gently  in  re- 
moving it  from  and  returning  it  to  the  case.  It  is  always 
best  to  place  the  hands  beneath  the  leveling  base  in  hand- 
ling the  detached  instrument.  Considerable  patience  is 
sometimes  required  to  close  the  lid  after  returning  the  in- 
strument. 

Mounting  the  Instrument.— See  that  the  instrument 
is  securely  attached  to  the  tripod  before  shouldering  it.  Un- 
due haste  in  this  particular  sometimes  results  in  costly 
accidents.  When  screwing  the  instrument  on  the  tripod 
head,  it  should  be  turned  in  a  reverse  direction  until  a  slight 
jar  is  felt,  indicating  that  the  threads  are  properly  engaged. 
Sunshade.— Always  attach  the  sunshade  regardless  of 
the  kind  of  weather.  The  sunshade  is  a  part  of  the  telescope 
tube  and  the  adjustment  of  a  delicate  instrument  may 
sometimes  be  affected  by  its  absence.  In  attaching  or  re- 
moving the  sunshade  or  object  glass  cap,  always  hold  the 
telescope  tube  firmly  with  one  hand  and  with  the  other 
twist  the  shade  or  cap  to  the  rii/lit  to  avoid  unscrewing  the 
object  glass  cell. 

Carrying  the  Instrument.— Do  not  carry  the  instru- 
ment on  the  shoulder  in  passing  through  doors  or  in  climb- 
ing fences.  Before  shouldering  the  instrument,  the  prin- 
cipal motions  should  be  slightly  clamped;  with  the  transit, 
clamp  the  telescope  on  the  line  of  centers;  and  with  the 
level,  when  the  telescope  is  hanging  down.  In  passing 
through  timber  with  low  branches,  give  special  attention 
to  the  instrument.  Before  climbing  a  fence,  set  the  instru- 
ment on  the  opposite  side  with  tripod  legs  well  spread. 

Setting  Up  in  the  Field.— When  setting  up  in  the  field, 
bring  the  tripod  legs  to  a  firm  bearing  with  the  plates  ap- 
proximately level.  Give  the  tripod  legs  additional  spread 
in  windy  weather  or  in  places  where  the  instrument  may 
be  subject  to  vibration  or  other  disturbance.  On  side-hill 


4  GENERAL  INSTRUCTIONS. 

work  place  one  leg  up  hill.  With  the  level,  place  two 
tripod  shoes  on  the  general  direction  of  the  line  of  levels. 

Exposure  of  Instrument.— Do  not  expose  the  instru- 
ment to  rain  or  dampness.  In  threatening  weather  the 
waterproof  bag  should  be  taken  to  the  field.  Should  the 
instrument  get  wet,  wipe  it  thoroughly  dry  before  return- 
ing it  to  the  case.  Protect  the  instrument  from  dust  and 
dirt,  and  avoid  undue  exposure  to  the  burning  action  of  the 
sun.  Avoid  subjecting  it  to  sudden  changes  of  tempera- 
ture. In  cold  weather  when  bringing  an  instrument  in- 
doors cover  the  instrument  with  the  bag  or  return  it  to 
the  case  immediately  to  protect  the  lenses  and  graduations 
from  condensed  moisture. 

Guarding  the  Instrument.— Never  leave  an  instrument 
unguarded  in  exposed  situations,  such  as  in  pastures,  near 
driveways,  or  where  blasting  is  in  progress.  Never  leave 
an  instrument  standing  on  its  tripod  over  night  in  a  room. 

Manipulation  of  Instrument.— Cultivate  from  the  very 
beginning  the  habit  of  delicate  manipulation  of  the  instru- 
ment. Many  parts,  when  once  impaired,  can  never  be  re- 
stored to  their  original  condition.  Rough  and  careless 
treatment  of  field  instruments  is  characteristic  of  the  un- 
skilled observer.  Should  any  screw  or  other  part  of  the  in- 
strument work  harshly,  call  immediate  attention  to  it  so 
that  repairs  may  be  made.  Delay  in  such  matters  is  very 
destructive  to  the  instrument. 

Foot  Screws. — In  leveling  the  instrument,  the  foot  screws 
should  be  brought  just  to  a  snug  bearing.  If  the  screws  are 
too  loose,  the  instrument  rocks,  and  accurate  work  can  not 
be  done;  if  too  tight,  the  instrument  is  damaged,  and  the 
delicacy  and  accuracy  of  the  observations  are  reduced.  Much 
needless  wear  of  the  foot  screws  may  be  avoided  if  the 
plates  are  brought  about  level  when  the  instrument  is  set 
up.  With  the  level,  a  pair  of  foot  screws  should  be  shifted 
to  the  general  direction  of  the  back  or  fore  sight  before 
leveling  up. 

Eyepiece. — Before  beginning  the  observations,  focus  the 
eyepiece  perfectly  on  the  cross-hairs.  This  is  best  done  by 
holding  the  note  book  page,  handkerchief,  or  other  white 
object  a  foot  or  so  in  front  of  the  object  glass  so  as  to  ilium- 


FIELD  EQUIPMENT.  5 

inate  the  hairs;  and  then,  by  means  of  the  eyepiece  slide, 
focus  the  microscope  on  a  speck  of  dust  on  the  cross-hairs 
near  the  middle  of  the  field.  To  have  the  focusing  true  for 
natural  vision,  the  eye  should  be  momentarily  closed  sev- 
eral times  between  observations  in  order  to  allow  the 
lenses  of  the  eye  to  assume  their  normal  condition.  The 
omission  of  this  precaution  strains  the  eye  and  is  quite  cer- 
tain to  cause  parallax.  After  the  eyepiece  is  focused  on  the 
cross-hairs,  test  for  parallax  by  sighting  at  a  well  denned  ob- 
ject and  observing  whether  the  cross-hairs  seem  to  move 
as  the  eye  is  shifted  slightly. 

Clamps.— Do  not  overstrain  the  clamps.  In  a  well  de- 
signed instrument  the  ears  of  the  clamp  screw  are  purpose- 
ly made  small  to  prevent  such  abuse.  Find  by  experiment 
just  how  tight  to  clamp  the  instrument  in  order  to  prevent 
slipping,  and  then  clamp  accordingly. 

Tangent  Screws.— Use  the  tangent  screws  only  for 
slight  motions.  To  secure  even  wear  the  screws  should 
be  used  equally  in  all  parts  of  their  length.  The  use  of  the 
wrong  tangent  movement  is  a  fruitful  source  of  error  with 
beginners. 

Adjusting  Screws.— Unless  the  instrument  is  assigned 
expressly  for  adjustment,  do  not  disturb  the  adjusting 
screws. 

Magnetic  Needle. — -Always  lift  the  needle  before  should- 
ering the  instrument.  Do  not  permit  tampering  with  the 
needle.  If  possible,  avoid  subjecting  the  needle  to  mag- 
netic influences,  such  as  may  exist  on  a  trolley  car.  Should 
the  needle  become  reversed  in  its  polarity  or  require  re- 
magnetization,  it  may  be  removed  from  the  instrument  and 
brought  into  the  magnetic  field  of  a  dynamo  or  electric 
motor  for  several  minutes,  the  needle  being  jarred  slightly 
during  the  exposure;  or  a  good  bar  or  horshoe  magnet  may 
be  used  for  the  same  purpose.  The  wire  coil  counterbalance 
on  the  needle  will  usually  require  shifting  after  the  fore- 
going process. 

Lenses.— Do  not  remove  or  rub  the  lenses  of  the  tele- 
scope. Should  it  be  alwiliitcli/  mvi-xxdrii  to  clean  a  lens,  use 
a  very  soft  rag  with  caution  to  avoid  scratching  or  marring 
the  polished  surface.  Protect  the  lenses  from  flying  sand 


6  GENERAL  INSTRUCTIONS. 

and  dust,  which  in  time  seriously  affect    the    definition    of 
the  telescope. 

Plumb  Bob. — Do  not  abuse  the  point  of  the  plumb  bob 
and  avoid  needless  knots  in  the  plumb  bob  string. 

Cleaning  Tripod  Shoes.— Remove  the  surplus  soil  from 
the  tripod  shoes  before  bringing  the  instrument  indoors. 

Leveling  Rods. — Leveling  rods  and  stadia  boards  should 
not  be  leaned  against  trees  or  placed  where  they  may  fall. 
Avoid  injury  to  the  clamps,  target  and  graduations.  Do  not 
mark  the  graduations  with  pencil  or  otherwise.  Avoid 
needless  exposure  of  the  rod  to  moisture  or  to  the  sun. 

Flag  Poles. — Flag  poles  should  not  be  unduly  strained, 
and  their  points  should  be  properly  protected. 

Chains  and  Tapes. — Chains  should  not  be  jerked.  Avoid 
kinks  in  steel  tapes,  especially  during  cool  weather.  When 
near  driveways,  in  crowded  streets,  etc.,  use  special  care  to 
protect  the  tape.  Band  tapes  will  be  done  up  in  5-foot 
loops,  figure  8  form,  unless  reels  are  provided.  Etched  tapes 
should  be  wiped  clean  and  dry  at  the  end  of  the  day's  work. 
Axes  and  Hatchets. — Axes  and  hatchets  will  be  em- 
ployed for  their  legitimate  purposes  only.  Their  wanton 
use  in  clearing  survey  lines  is  forbidden,  and  their  use  at  all 
for  such  purpose  on  private  premises  must  he  governed 
xtririli/  by  the  rights  of  the  owner. 

Stakes.— The  consumption  of  stakes  should  be  controlled 
by  reasonable  economy.  Surplus  stakes  will  be  returned  to 
the  general  store.  For  the  protection  of  mowing  machines 
in  meadows,  etc.,  hub  stakes  should  be  driven  flush  with 
the  surface  of  the  ground,  and  other  stakes  should  be  left 
high  enough  to  be  visible.  Whenever  practicable,  stakes 
which  may  endanger  machines  should  be  removed  after 
serving  the  purpose  for  which  they  were  set. 


FIELD  NOTES. 

Scope  of  Field  Notes.— The  notes  should  be  a  complete 
record  of  each  day's  work  in  the  field.  In  addition  to  the 
title  of  the  problem  and  the  record  of  the  data  observed, 
the  field  notes  should  include  the  date,  weather,  organiza- 
tion of  party,  equipment  used,  time  devoted  to  the  prob- 


FIELD  NOTES.  7 

lem,  and  any  other  information  which  is  at  all  likely  to  be 
of  service  in  connection  with  the  problem.  No  item  proper- 
ly belonging  to  the  notes  should  be  trusted  to  memory. 
Should  the  question  arise  as  to  the  desirability  of  any  item, 
it  is  always  safe  to  include  it.  The  habit  of  rigid  self  criti- 
cism of  the  field  notes  should  be  cultivated. 

Character  of  Notes.— The  field  notes  should  have  char- 
acter and  force.  As  a  rule,  the  general  character  of  the 
student's  work  can  be  judged  with  considerable  certainty 
by  the  appearance  of  his  field  notes.  A  first-class  page  of 
field  notes  always  commands  respect,  and  tends  to  estab- 
lish and  stimulate  confidence  in  the  recorder.  The  notes 
should  be  arranged  systematically. 

Interpretation  of  Notes.— The  field  notes  should  have 
one  and  only  one  reasonable  interpretation,  and  that  the 
correct  one.  They  should  be  perfectly  legible  and  easily 
understood  by  anyone  at  all  familiar  with  such  matters. 

Original  Notes.— Each  student  must  keep  complete  notes 
of  each  problem.  Field  notes  must  not  be  taken  on  loose 
slips  or  sheets  of  paper  or  in  other  note  books,  but  the 
orij/huil  record  must  be  put  in  the  prescribed  field  note  book 
durlnij  the  i»'o<j>'exx  of  tlie  ficlil  irork. 

Field  Note  Book. — The  field  record  must  be  kept  in  the 
prescribed  field  note  book.  For  ease  of  identification  the 
name  of  the  owner  will  be  printed  in  bold  letters  at  the  top 
of  the  front  cover  of  the  field  note  book. 

Pencil.— To  insure  permanency  all  notes  will  be  kept 
with  a  hard  pencil,  preferably  a  4H.  The  pencil  should  be 
kept  well  sharpened  and  used  with  sufficient  pressure  to 
indent  the  surface  of  the  paper  somewhat. 

Title  Page.— An  appropriate  title  page  will  be  printed 
on  the  first  page  of  the  field  note  book. 

Indexing  and  Cross  Referencing.— A  systematic  index 
of  the  field  notes  will  be  kept  on  the  four  pages  following 
the  title  page.  Related  notes  on  different  pages  will  be  lib- 
erally and  plainly  cross  referenced.  The  pages  of  the  note 
book  will  be  numbered  to  facilitate  indexing. 

Methods  of  Recording  Field  Notes.— There  are  three 
general  methods  of  recording  field  notes,  namely,  (1)  by 


8  GENERAL  INSTRUCTIONS. 

sketch,  (2)  by  description  or  narration,  and  (3)  by  tabula- 
tion. It  is  not  uncommon  to  combine  two  or  perhaps  all 
three  of  these  methods  in  the  same  problem  or  survey. 

Form  of  Notes.— All  field  notes  must  be  recorded  in  the 
form  below,  except  where  circumstances  require  modifi- 
cation. If  no  form  is  given,  the  student  will  devise  one 
suited  to  the  needs  of  the  particular  problem. 


Lettering. — Field  notes  will  be  printed  habitually  in  the 
''Engineering  N«ws"  style  of  freehand  lettering,  as  treated 
in  Reinhardt's  "Freehand  Lettering."  The  body  of  the  field 
notes  will  be  recorded  in  the  slanting  letter  and  the  head- 
ings will  be  made  in  the  upright  letter.  The  former  slants 
to  the  right  1:2.5  and  the  so-called  upright  letter  is  made 
to  slant  to  the  left  slightly,  say  1:25.  Lower  case  letters 
will  be  used  in  general,  capitals  being  employed  for  initials 
and  important  words,  as  required.  In  the  standard  field 


FIELD  NOTES.  9 

note  alphabet  the  height  of  lower  case  letters  a,  c,  e,  i,  ra, 
n,  etc.,  is  3-50  (say  1-16)  inch,  and  the  height  of  lower  case 
b,  d,  t,  g,  h,  etc.,  and  of  all  capital  letters  and  all  numerals 
is  5-50  (1-10)  inch;  lower  case  t  is  made  four  units  (4-50) 
inch  high.  This  standard  accords  with  best  current  prac- 
tice and  is  based  upon  correct  economic  principles.  (See 
chapter  giving  discussion  of  freehand  lettering.)  The 
standard  field  note  alphabets  are  given  on  the  bookmark 
scale  which  accompanies  this  manual.  The  student  is  ex- 
pected to  make  the  most  of  this  opportunity  to  secure  a 
liberal  amount  of  practice  in  freehand  lettering. 

Field  Note  Sketches.— Sketches  will  be  used  liberally 
in  the  notes  and  will  be  made  in  the  field.  If  desired,  a  ruler 
may  be  used  in  drawing  straight  lines,  but  the  student  is 
urged  to  acquire  skill  at  once  in  making  good  plain  free- 
hand sketches.  The  field  sketches  should  be  bold  and  clear, 
in  fair  proportion,  and  of  liberal  size  so  as  to  avoid  con- 
fusion of  detail.  The  exaggeration  of  certain  details  in  a 
separate  sketch  sometimes  adds  greatly  to  the  clearness  of 
the  notes.  The  sketches  should  be  supplemented  by  de- 
scriptive statements  when  helpful,  and  important  points  of 
the  sketch  should  be  lettered  for  reference.  The  precise 
scaling  of  sketches  in  the  field  note  book,  while  sometimes 
necessary,  is  usually  undesirable  owing  to  the  time  con- 
sumed. It  is  also  found  that  undue  attention  to  the  draft- 
ing of  the  sketch  is  very  apt  to  occupy  the  mind  and  cause 
omissions  of  im'portant  numerical  data.  Since  recorded 
figures  and  not  the  size  of  the  field  sketch  itself  must  usual- 
ly be  employed  in  the  subsequent  use  of  the  notes,  it  is  im- 
portant to  review  the  record  before  learing  tlie  field  to  detect 
omissions  or  inconsistencies.  Making  sketches  on  loose 
sheets  or  in  other  books  and  subsequently  copying  them 
into  the  regular  field  book  is  very  objectionable  practice 
and  will  not  be  permitted  in  the  class  work.  Copies  of  field 
notes  or  sketches  are  never  as  trustworthy  as  the  original 
record  made  diiritif/  the  progress  of  the  field  work.  In  very 
rapid  surveys  where  legibility  of  the  original  record  must 
perhaps  suffer  somewhat,  it  is  excellent  practice  to  tran- 
scribe the  notes  at  once  to  a  neighboring  page,  thus  pre- 
serving the  original  rough  notes  for  future  reference.  The 


10.  GENERAL  INSTRUCTIONS. 

original  has  more  weight  as  evidence,  but  the  neat  copy 
made  before  the  notes  are  "cold"  is  of  great  help  in  inter- 
preting them. 

Numerical  Data. — The  record  of  numerical  data  should 
be  consistent  with  the  precision  of  the  survey.  In  obser- 
vations of  the  same  class  a  uniform  number  of  decimal 
places  should  be  recorded.  When  the  fraction  in  a  result 
is  exactly  one-half  the  smallest  unit  or  decimal  place  to  be 
observed,  record  the  even  unit.  Careful  attention  should 
be  given  to  the  legibility  of  numerals.  This  is  a  matter  in 
which  the  beginner  is  often  very  weak.  This  defect  can  be 
corrected  best  by  giving  studious  attention  and  practice  to 
both  the  form  and  vertical  alinement  of  tabulated  numerals. 
Erasures. — Erasures  in  the  field  notes  will  be  strictly 
avoided.  Should  a  figure  be  incorrectly  recorded,  it  should 
be  crossed  out  and  the  correct  entry  made  near  by.  The 
neat  cancellation  of  an  item  in  the  notes  inspires  confi- 
dence, but  evidence  of  an  erasure  or  alteration  casts  doubt 
upon  their  genuineness.  When  a  set  of  notes  becomes  so 
confused  that  erasure  seems  desirable,  it  should  be  tran- 
scribed, usually  on  another  page.  Rejection  of  a  page  of 
notes  should  be  indicated  by  a  neat  cross  mark,  and  cross 
reference  should'  be  made  between  the  two  places. 

Office  Copies. — Office  copies  of  field  notes  will  be  sub- 
mitted promptly,  as  required.  These  copies  must  be  actual 
transcripts  from  the  original  record  contained  in  the  field 
note  book  of  the  individual  submitting  the  copy.  When 
office  copies  are  made,  a  memorandum  of  the  fact  should 
be  entered  on  the  page  of  the  field  note  book.  When  so 
specified,  the  office  copies  will  be  executed  in  india  ink. 

Criticism  of  Field  Notes. — The  field  notes  must  be  kept 
in  shape  for  inspection  at  any  time,  and  be  submitted  on 
call.  All  calculations  and  reductions  must  be  kept  up  to 
date.  The  points  to  which  chief  attention  should  be  direct- 
ed in  the  criticism  of  the  field  notes  are  indicated  in  the 
following  schedule.  The  student  is  expected  to  criticise  his 
own  notes  and  submit  them  in  as  perfect  condition  as  pos- 
sible. For  simplicity  the  criticisms  will  be  indicated  by 
stamping  on  the  note  book  page  the  reference  letters  and 
numbers  shown  in  the  schedule. 


FIELD  NOTES.  11 

SCHEDULE    OF     POINTS    FOR    THE     CRITICISM      OF 
FIELD  NOTE  BOOKS. 

A.  SUBJECT  MATTER. 

(1)  General: 

(a)  Descriptive  title  of  problem. 

(b)  Date. 

(c)  Weather. 

(d)  Organization  of  party. 

(e)  Equipment  used. 

(f)  Time  devoted  to  the  problem. 

(g)  Indexing  and  cross  referencing, 
(h)  Page  numbering. 

(i)  Title  page. 

(j)  Identification  of  field  note  book. 

(2)  Record  of  Data: 

(a)  Accuracy. 

(b)  Completeness. 

(c)  Consistency. 

(d)  Arrangement. 

(e)  Originality. 

B.  EXECUTION. 

(1)  Lettering: 

(a)  Style.     ("Engineering  News.") 

(b)  Size,    (a,  c,  e,  i,  etc.,  3-50  (say  1-16)  inch  high;  b,  d, 
f,  g,  etc.,     A,  B,  C,  etc.,  and  1,  2,  3,  etc.,  5-50  (1-10)  inch 
high;  t,  4-50  inch.) 

(c)  Slant.     (In  body  of  notes,  "slanting,"  1:2.5  right;   in 
headings,  "upright,"  about  1:25  to  left.) 

(d)  Form.     (See  Reinhardt's  "Freehand  Lettering.") 

(e)  Spacing.    (Of  letters  in  words;  of  numerals;  of  words; 
balancing  in  column  or  across  page.) 

(f)  Alinement.  (Horizontal;   vertical.) 

(g)  Permanency.     (Use  sharp  hard  pencil  with  pressure.) 

(2)  Sketches. 

(a)  To  be  bold,  clear  and  neat. 

(b)  To  be  ample  in  amount. 

(c)  To  be  of  liberal  size. 

(d)  To  be  in  fair  proportion. 

(e)  To  be  made  freehand. 

(f)  To  be  made  in  the  field. 


12  GENERAL  INSTRUCTIONS. 

Importance  of  Office  Work.— Capable  office  men  are 
comparatively  rare.  Skill  in  drafting  and  computing  is 
within  the  reach  of  most  men  who  will  devote  proper  time 
and  effort  to  the  work.  Men  who  are  skillful  in  both  field 
and  office  work  have  the  largest  opportunity  for  advance- 
ment. 

Calculations. — All  calculations  and  reductions  of  a  per- 
manent character  must  be  shown  in  the  field  note  book  in 
the  specified  form.  Cross  references  between  field  data  and 
calculations  should  be  shown.  Consistency  between  the 
precision  of  computed1  results  and  that  of  the  observed  data 
should  be  maintained.  Computed  results  should  be  verified 
habitually,  and  the  verified  results  indicated  by  a  check 
mark.  Since  most  computers  are  prone  to  repeat  the  same 
error,  it  is  desirable  in  checking  calculations  to  employ  in- 
dependent methods  and  to  follow  a  different  order.  A 
fruitful  source  of  trouble  is  in  the  transcript  of  data,  and 
this  should  be  checked  first  when  reviewing  doubtful  cal- 
culations. Skilled  computers  give  much  attention  to 
methodical  arrangement,  and  to  contracted  methods  of 
computing  and  verifying  results.  Familiarity  with  the 
slide  rule  and  other  labor  saving  devices  is  important. 
(See  chapter  on  methods  of  computing.) 

Drafting  Room  Equipment.— The  student  is  respon- 
sible for  the  proper  use  and  care  of  drafting  room  furniture 
and  equipment  provided  for  his  use. 

Drafting.— The  standard  of  drafting  is  that  indicated  in 
Reinhardt's  "Technic  of  Mechanical  Drafting." 

Drafting  Room  Decorum.— The  decorum  of  the  student 
in  the  drafting  room  will  conform  to  that  observed  in  first- 
class  city  drafting  offices. 


CHAPTER  II. 
THE  CHAIN  AND  TAPE. 


METHODS  OF  FIELD  WORK. 

Units  of  Measure.— In  the  United  States  the  foot  is  used 
by  civil  engineers  in  field  measurements  Fractions  of  a 
foot  are  expressed  decimally,  the  nearest  0.1  being  taken 
in  ordinary  surveys,  and  the  nearest  0.01  foot  (say  1-8 
inch)  in  more  refined  work. 

In  railroad  and  similar  "line"  surveys  in  which  a  station 
stake  is  set  every  100  feet,  the  unit  of  measure  is  really  100 
feet  instead  of  the  foot.  The  term  "station"  was  originally 
applied  only  to  the  actual  point  indicated  by  the  numbered 
stake,  but  it  is  now  universal  practice  in  this  country  to 
use  the  word  station  in  referring  to  either  the  point  or  the 
100-foot  unit  distance.  A  fractional  station  is  called  a 
"plus"  for  the  reason  that  a  plus  sign  is  used  to  mark  the 
decimal  point  for  the  100-foot  unit,  the  common  decimal 
point  being  reserved  for  fractions  of  a  foot.  The  initial  or 
starting  stake  of  such  a  survey  is  numbered  0. 

The  100-foot  chain  is  commonly  called  the  "engineers' 
chain"  to  distinguish  it  from  the  66-foot  or  100-link  chain 
which  is  termed  the  "surveyors'  chain"  because  of  its 
special  value  in  land  surveys  involving  acreage.  The  latter 
is  also  called  the  Gunter  chain  after  its  inventor,  and  is 
otherwise  known  as  the  four-rod  or  four-pole  chain.  British 
engineers  use  the  Gunter  chain  for  both  line  and  land  sur- 
veys. The  United  States  rectangular  surveys  were  made 
throughout  with  the  66- foot  chain. 

In  the  Spanish-American  countries  the  vara  is  generally 
used  in  land  surveys.  The  Castilian  vara  is  32.8748  inches 
long,  but  the  state  of  California  has  adopted  32.372  inches, 
and  Texas  33  1-3  inches,  as  the  legal  length  of  the  vara. 

While  the  metric  system  is  used  exclusively  or  in  part  in 
each  of  the  several  United  States  government  surveys,  ex- 
cept the  public  land  surveys,  little  or  no  progress  has  been 
made  toward  its  introduction  in  other  than  government 
surveys. 


14 


THE  CHAIN  AND  TAPE. 


Linear  Measuring  Instruments.— Two  general  types  of 
linear  measuring  devices  are  used  by  surveyors,  viz.,  the 
common  chain  and  the  tape.  There  are  several  kinds  of 
each,  according  to  the  length,  material  and  method  of  grad- 
uation. 


Fig.  1. 


The  common  chain  is  made  up  of  a  series  of  links  of 
wire  having  loops  at  the  ends  and  connected  by  rings  so  as 
to  afford  flexibility.  The  engineers'  chain  is  shown  in  (a), 
Fig.  1.  the  illustration  being  that  of  a  50-foot  chain,  or  one- 
half  the  length  generally  used.  The  surveyors'  or  Gunter 


METHODS  OF  FIELD  WORK.  15 

chain  is  shown  in  (b),  Fig.  1.  In  the  common  chain  the 
end  graduation  is  the  center  of  the  cross  bar  of  the  handle, 
and  every  tenth  foot  or  link  is  marked  by  a  notched  brass 
tag.  In  the  100-foot  or  100-link  chain  the  number  of  points 
on  the  tag  indicates  the  multiple  of  ten  units  from  the  near- 
er end,  and  a  circular  tag  marks  the  middle  of  the  chain. 
The  chain  is  done  up  hour  glass  shape,  as  shown  in  the  cut. 

Chaining  pins  made  of  steel  wire  are  used  in  marking  the 
end  of  the  chain  or  tape  in  the  usual  process  of  linear 
measurement.  A  set  of  pins  usually  numbers  eleven,  as 
indicated  at  (c),  Fig.  1.  The  pins  are  carried  on  a  ring 
made  of  spring  steel  wire. 

The  flat  steel  band,  shown  in  (d)  and  fe),  Fig.  1,  is  the 
best  form  of  measuring  device  for  most  kinds  of  work.  The 
band  tape  is  usually  100  feet  long.  The  end  graduations  of 
the  band  tape  are  usually  indicated  by  brass  shoulders, 
which  should  point  in  the  same  direction,  as  shown  in  (f), 
Fig.  1.  The  100-foot  band  tape  is  commonly  graduated 
every  foot  of  its  length,  and  the  end  foot  to  every  0.1  foot, 
every  fifth  foot  being  numbered  on  a  brass  sleeve.  Brass 
rivets  are  the  most  common  mode  of  graduating  this  tape. 
The  band  tape  may  be  rolled  up  on  a  special  reel,  as  indi- 
cated in  (d)  and  (e),  although  some  engineers  dispense 
with  the  reel  and  do  up  the  tape  in  the  form  of  the  figure  8 
in  loops  of  five  feet  or  so. 

The  steel  tapes  shown  in  (g)  and  (h)  have  etched  gradu- 
ations. This  style  of  tape  is  commonly  graduated  to  0.01 
foot  or  1-8  inch.  It  is  more  fragile  than  the  band  tape  and" 
is  commonly  used  on  more  refined  work.  The  form  of  the 
case  shown  in  (h)  has  the  advantage  of  allowing  the  tape  to 
dry  if  wound  up  while  damp. 

The  "metallic"  tape,  (i),  Fig.  1,  is  a  woven  linen  line  hav- 
ing fine  brass  wire  in  the  warp. 

The  steel  tape  is  superior  to  the  common  chain  chiefly 
because  of  the  permanency  of  its  length.  The  smoothness 
and  lightness  of  the  steel  tape  are  often  imporrant  advan- 
tages, although  the  latter  feature  may  be  a  serious  draw- 
back at  times.  The  tape  is  both  easier  to  break  and  more 
difficult  to  mend  than  the  common  chain. 


16  THE  CHAIN  AND  TAPE. 

Chaining. — In  general,  the  horizontal  distance  is  chained. 
Two  persons,  called  head  and  rear  chainmen,  are  required. 
The  usual  process  is  as  follows: 

The  line  to  be  chained  is  first  marked  with  range  poles. 
The  head  chainman  casts  the  chain  out  to  the  rear,  and 
after  setting  one  marking  pin  at  the  starting  point  and 
checking  up  the  remaining  ten  pins  on  his  ring,  steps 
briskly  to  the  front.  The  rear  chainman  allows  the  chain 
to  pass  through  his  hands  to  detect  kinks  and  bent  links. 
Just  before  the  full  length  is  drawn  out,  the  rear  chainman 
calls  "halt,"  at  which  the  head  chainman  turns,  shakes  out 
the  chain  and  straightens  it  on  the  true  line  under  the 
direction  of  the  rear  chainman.  In  order  to  allow  a  clear 
sight  ahead,  the  front  chainman  should  hold  the  chain 
handle  with  a  pin  in  his  right  hand  well  away  from  his 
body,  suporting  the  right  elbow  on  the  right  knee,  if  de- 
sired. The  rear  chainman  holds  the  handle  in  his  left  hand 
approximately  at  the  starting  point  and  motions  with  his 
right  to  the  head  chainman,  his  signals  being  distinct  both 
as  to  direction  and  amount.  Finally,  when  the  straight 
and  taut  chain  has  been  brought  practically  into  the  true 
line,  the  rear  chainman,  slipping  the  handle  behind  the  pin 
at  the  starting  point  with  his  left  hand,  and  steadying  the 
top  of  the  pin  with  his  right,  calls  out  "stick."  The  head 
chainman  at  this  instant  sets  his  pin  in  front  of  the  chain 
handle  and  responds  "stuck,"  at  which  signal  and  not  before 
the  rear  chainman  pulls  the  pin. 

Both  now  proceed,  the  rear  chainman  giving  the  prelim- 
inary "halt"  signal  as  he  approaches  the  pin  just  set  by 
the  head  chainman.  The  chain  is  lined  up,  stretched,  the 
front  pin  set,  and  the  rear  pin  pulled  on  signal,  as  described 
for  the  first  chain  length.  This  process  is  repeated  until 
the  head  chainman  has  set  his  tenth  pin,  when  he  calls 
"out"  or  "tally,"  at  which  the  rear  chainman  walks  ahead, 
counting  his  pins  as  he  goes  and,  if  there  are  ten,  transfers 
them  to  the  head  chainman  who  also  checks  them  up  and 
replaces  them  on  his  ring.  A  similar  check  in  the  pins  may 
be  made  at  any  time  by  remembering  that  the  sum,  omit- 
ting the  one  in  the  ground,  should  be  ten.  This  safeguard 
should  be  taken  often  to  detect  loss  of  pins.  The  count  of 
tallies  should  be  carefully  kept. 


METHODS   OF  FIELD  WORK.  17 

When  the  end  of  the  line  is  reached,  the  rear  chainman 
steps  ahead,  and  reads  the  fraction  at  the  pin,  noting  the 
units  with  respect  to  the  brass  tags  on  the  chain.  The 
number  of  pins  in  the  hand  of  the  rear  chainman  indicates 
the  number  of  applications  of  the  chain  since  the  starting 
or  last  tally  point.  A  like  method  is  used  in  case  inter- 
mediate points  are  to  be  noted  along  the  line. 

On  sloping  ground  the  horizontal  distance  may  be  ob- 
tained either  by  leveling  the  chain  and  plumbing  down 
from  the  elevated  end,  or  by  measuring  on  the  slope  and 
correcting  for  the  inclination.  In  ordinary  work  the  former 
is  preferred,  owing  to  its  simplicity.  In  "breaking  chain" 
up  or  down  a  steep  slope,  the  head  chainman  first  carries 
the  full  chain  ahead  and  places  it  carefully  on  the  true  line. 
A  plumb  bob,  range  pole  or  loaded  chaining  pin  should  be 
used  in  plumbing  the  points  up  or  down.  The  segments  of 
the  chain  should  be  in  multiples  of  ten  units,  as  a  rule,  and 
the  breaking  points  should  be  "thumbed"  by  both  chain- 
men  to  avoid  blunders.  Likewise,  special  caution  is  re- 
quired to  avoid  confusion  in  the  count  of  pins  during  this 
process. 

The  general  method  of  measuring  with  the  band  tape  is 
much  the  same  as  with  the  common  chain.  The  chief  dif- 
ference is  due  to  the  fact  that  the  handle  of  the  tape  extends 
beyond  the  end  graduation,  so  that  it  is  more  convenient 
for  the  head  chainman  to  hold  the  handle  in  his  left  hand 
and  rest  his  left  elbow  on  his  left  knee,  setting  the  pin  with 
his  right  hand.  Another  difference  is  in  the  method  of 
reading  fractions.  It  is  best  to  read  the  fraction  firxf  l>u 
estimation,  as  with  the  chain,  making  sure  of  the  feet;  then 
shifting  the  tape  along  one  foot,  getting  an  exact  decimal 
record  of  the  fraction  by  means  of  the  end  foot  graduated 
to  tenths;  the  nearest  0.01  foot  is  estimated,  or  in  especially 
refined  work,  read  by  scale. 

In  railroad  and  similar  line  surveys,  chaining  pins  are 
usually  dispensed  with  and  the  ends  of  the  chain  are  indi- 
cated by  numbered  stakes.  The  stake  marked  0  corre- 
sponds to  the  pin  at  the  starting  point,  and  the  station 
stakes  are  marked  thence  according  to  the  number  of 
100-foot  units  laid  off. 


18 


THE  CHAIN  AND  TAPE. 


Perpendiculars.— Perpendiculars  may  be  erected  and 
let  fall  with  the  chain  or  tape  by  the  following  methods. 

(a)  By  the  3:4:5  method,  shown  in  (a).  Fig.  2,  in  which 
a  triangle  having  sides  in  the  ratio  stated,  is  constructed. 

(b)  By  the  chord  bisection  method,  shown  in  (b),  Fig.  2, 
in  which  a  line  is  passed  from  the  bisecting  point  of  the 
chord  to  the  center  of  the  circle,  or  vice  \ersa. 

(c)  By  the  semicircle  method,  shown  in   (c),   Fig.   2,   in 
which  a  semicircle  is  made  to  contain  the  required  perpen- 
dicular. 

The  first  method  corresponds  to  the  use  of  the  triangle 
in  drafting.  Good  intersections  are  essential  in  the  second 
and  third  methods.  Results  may  be  verified  either  by  using 
another  process,  or  by  repeating  the  same  method  with  the 
measurements  or  position  reversed,  as  indicated  in  (d), 
Fig.  2. 

In  locating  a  perpendicular  from  a  remote  point,  the  ratio 
method  shown  in  (e),  Fig.  2,  may  be  used;  or  a  careful  trial 
perpendicular  may  be  erected  at  a  point  estimated  by  plac- 
ing the  heels  squarely  on  line  and  swinging  the  arms  to  the 
front,  then  proving  by  precise  method. 


Fig.  2. 


METHODS  OF  FIELD  WORK.  19 

Parallels.— Parallels  may  be  laid  off  with  the  chain  in 
various  ways,  a  few  of  the  simpler  of  which  are: 

(a)  By  equal  distances,  as  in   (a),  Fig.  3,  in  which  two 
equal  distances  are  laid  off,  usually  at  right  angles  to  the 
given  line. 

(b)  By  similar  triangles,  as  in  (b)  and  (c),  Fig.  3.     The 
ratio  may,  of  course,  have  any  value. 

(c)  By  alternate  angles,  as  in  (d),  Fig.    3,    in    which   two 
equal  angles  are  laid  off  in  alternation. 

The  first  method  is  adapted  to  laying  off  a  rectangle,  as 
in  staking  out  a  building,  in  which  case  a  good  check  is 
found  in  the  equality  of  the  diagonals.  Precision  of  aline- 
ment  is  important,  especially  where  a  line  is  prolonged. 

Angles.— Angles  may  be  determined  by  linear  measure- 
ments in  the  following  ways: 

(a)  By  the  chord  method,  shown  in  (a),  Fig.  4,  in  which 
the  radius  is  laid  off  on  the  two  lines  forming  the  angle, 
and  the  chord  measured. 

(b)  The  tangent  method,  shown  in  (b),  Fig.  4,  in  which 
a  perpendicular  is  erected  at  one  end  of  the  radius,  and  the 
length  of  the  perpendicular  intercepted   by  the  two  lines 
measured. 

(c)  The  sine-cosine  method,   (c),  Fig.  4,  which  is  better 
suited  to  constructing  than  to  measuring  angles. 

The  chord  method  is  usually  the  most  satisfactory.  The 
tangent  method  may  be  applied  to  the  bisected  angle  when 
its  value  approaches  a  right  angle.  Measurement  of  the 
supplementary  angle  affords  an  excellent  check.  A  100-foot 
radius  is  commonly  used,  although  good  results  may  be  had 
with  the  50-foot  tape.  Careful  alinement  is  of  the  first  im- 
portance in  angular  measurements. 

It  is  sometimes  necessary  to  determine  angles,  at  least 
approximately,  when  no  tables  are  at  hand.  Fair  results 
may  be  had  on  smooth  ground  by  measuring  the  actual  arc 
struck  off  to  a  radius  of  57.3  feet. 

For  very  small  angles,  the  sine,  chord,  arc  and  tangent, 
(d),  Fig.  4,  are  practically  equal.  Thus,  sin  1°  is  .017452  and 
tan  1°,  .017455,  or  either  (say)  .01745,  or  1%  per  cent.  Also, 
arc  1'  is  .000291,  or  (say)  .0003  (three  zeros  three);  and,  arc 
1"  is  .00000485,  (say)  .000005  (five  zeros  five). 


20 


THE  CHAIN  AND  TAPE. 


Location  of  Points.— Points    are    located    in    surveying 
field  practice  in  the  following  seven  ways. 

(a)  By  rectangular    coordinates,    that    is,    by    measuring 
the  perpendicular   distance   from   the   required   point  to   a 
given  line,  and   the  distance   thence  along  the   line   to   a 
given  point,  as  in  (a),  Fig.  5. 

(b)  By  focal  coordinates  or  tie  lines,  that  is,  by  meas- 
uring the  distances  from  the  required  point  to  two  given 
points,  as  in  (b),  Fig.  5. 

(c)  By  polar  coordinates,  that  is,  by  measuring  the  angle 
between  a  given  line  and  a  line  drawn  from  any  given  point 
of  it  to  the  required  point;  and  also  the  length  of  this  latter 
line,  as  in  (c),  Fig.  5. 

(d)  By  modified  polar  coordinates,  that  is,  by  a  distance 
from  one  known  point  and  a  direction  from  another,  as  in 
(d),  Fig.  5. 

(e)  By  angular   intersection,   that  is,   by   measuring   the 
angles  made  with  a  given  line  by  two  other  lines  starting 
from  given  points   upon   it,   and   passing   through   the   re- 
quired point,  as  in  (e),  Fig.  5. 

(f)  By  resection,  that  is,  by  measuring  the  angles  made 
with  each  other  by  three  lines  of  sight  passing  from  the 
required  point  to  three  points,  whose  positions  are  known, 
as  in  (f),  Fig.  5. 

(g)  By  diagonal  intersection,  that  is,  by  two  lines  joining 
two  pairs  of  points  so  as  to  intersect  in  the  required  point, 
as  in  (g),  Fig.  5. 


Fig.  5, 


METHODS  OP  FIELD  WORK. 


In  each  of  these  methods,  except  (f),  the  point  is  deter- 
mined by  the  intersection  of  either  two  right  lines,  or  two 
circles,  or  a  right  line  and  a  circle. 

Methods  (a)  and  (b)  are  best  suited  to  chain  surveys; 
(c)  and  (d)  are  used1  most  in  the  location  of  railroad 
curves;  (e)  and  (f)  are  employed  chiefly  in  river  and  ma- 
rine surveys  for  the  location  of  soundings,  the  latter  being 
commonly  known  as  the  "three-point  problem;"  the  last 
method,  (g),  is  much  used  for  "referencing  out"  transit 
points  in  railroad  and  similar  construction  surveys. 

Location  of  Objects. — The  location  of  buildings  and 
topographic  objects  usually  involves  one  or  more  of  the 
foregoing  methods  of  locating  a  point. 

In  Fig.  6,  (a),  (b),  (c),  and  (d)  suggest  methods  of  locat- 
ing a  simple  form,  and  (e)  and  (f)  illustrate  more  complex 
cases. 

Tie  Line  Surveys. — For  many  purposes  tie  line  surveys, 
made  with  the  chain  or  tape  alone,  are  very  satisfactory. 
The  skeleton  of  such  surveys  is  usually  the  triangle,  the 
detail  being  filled  in  by  the  methods  just  outlined.  Much 
time  may  be  saved  by  carefully  planning  the  survey.  A  few 
typical  applications  of  the  tie  line  method  are  shown  in 
Fig.  7. 


JLJLJL 

HOC 


22 


THE  CHAIN  AND  TAPE. 


Ranging  in  Lines.— The  range  or  flag  pole  is  usually 
painted  with  alternate  feet  red  and  white,  and  the  lower 
end  is  shod  or  spiked.  A  temporary  form  of  range  pole, 
called  a  picket,  is  sometimes  cut  from  straight  sapplings. 

In  flagging  a  point,  the  spike  of  the  pole  is  placed  on  the 
tack  and  the  pole  plumbed  by  holding  it  symmetrically  be- 
tween the  tips  of  the  fingers  of  the  two  hands,  the  flagman 
being  squarely  behind  the  pole. 

In  hilly  or  timbered  country  the  two  land  corners  or  other 
points  between  which  it  is  desired  to  range  in  a  line,  are 
often  invisible  one  from  the  other.  In  many  cases  two  in- 
termediate points  C'  and  D',  (a),  Fig.  8,  may  be  found,  from 
which  the  end  points  B  and  A,  respectively,  are  visible;  so 
that  after  a  few  successive  linings  in,  each  by  the  ather, 
the  true  points,  C  and  D,  are  found. 

Otherwise,  as  shown  at  (b),  Fig.  8,  a  random  line  may 
be  run  from  A  towards  B.  The  trial  line  is  chained  and 
marked,  the  perpendicular  from  B  located,  and  points  inter- 
polated on  the  true  line. 

If  the  desired  line  is  occupied  by  a  hedge  or  other  ob- 
struction, an  auxiliary  parallel  line  may  be  established  in 
the  adjacent  road  or  field,  after  one  or  two  trials,  as  in  (c), 
Fig.  8. 

A  line  may  be  prolonged  past  an  obstacle  by  rectangular 
offsets  or  by  equilateral  triangles. 


Fig.  8. 


Fig.    9. 


Signals.— There  is  little  occasion  for  shouting  in  survey- 
ing field  work  if  a  proper  system  of  sight  signals  is  used. 
Each  signal  should  have  but  one  meaning  and  that  a  per- 
fectly distinct  one.  Signals  indicating  motion  should  at 


METHODS  OF  FIELD  WORK.  23 

once  show  clearly  both  the  direction  and  amount  of  motion 
desired.    Some  of  the  signals  in  common  use  are  as  follows: 

(a)  "Right"  or  "left,"— the  arm  is  extended  distinctly  in 
the  desired  direction  and  the  motion  of   the  forearm  and 
hand  is  graduated  to  suit  the  lateral  motion  required. 

(b)  "Up"  or  "down,"— the  arm  is  extended  laterally  and 
raised  or  lowered  distinctly  with  motions  to  suit  the  magni- 
tude of  the  movement  desired.     Some  levelers  use  the  left 
arm  for  the  "up"  signal  and  the  right  for  "down." 

(c)  "Plumb  the  pole  (or  rod),"— if  to  the  right,  that  arm 
is  held  vertically  with  hand  extended  and  the  entire  body, 
arm  included,  is  swung  distinctly  to  the  right,  or  vice  versa. 

(d)  "All  right,"— both  arms  are  extended  full  length  hori- 
zontally and  waved  vertically. 

(e)  "Turning  point"  or  "transit  point," — the  arm  is  swung 
slowly  about  the  head. 

(f)  "Give  line," — the  flagman  extends  both  arms  upward, 
holding  the  flag  pole  horizontally,  ending  with  the  pole  in 
its  vertical  position.     If  a  precise  or  tack  point  is  meant, 
the  signal  is  made  quicker  and  sharper. 

(g)  Numerals  are  usually  made  by  counted  vertical  swings 
with   the   arm   extended   laterally.     A   station    number   is 
given  with  the  right  hand  and  the  plus,  if  any,  with  the 
left;    or  a  rod    reading    in    like    manner.      The    successive 
counts  are  separated  by  a  momentary  pause,  emphasized,  if 
desired,  by  a  slight  swing  with  both  hands. 

Stakes  and  Stake  Driving.— A  flat  stake  is  used  to 
mark  the  stations  in  a  line  survey,  and  a  square  stake  or 
hub  to  mark  transit  stations,  (a)  and  (b),  Fig.  9.  The 
station  stake  is  numbered  on  the  rear  face,  and  the  hub  is 
witnessed  by  a  flat  guard  stake  driven  slanting  10  inches  or 
so  to  the  left,  Fig.  9.  The  numerals  should  be  bold  and 
distinct,  and  made  with  keel  or  waterproof  crayon,  pressed 
into  the  surface  of  the  wood.  , 

Having  located  a  point  approximately  with  the  flag  pole, 
the  stake  should  be  driven  truly  plumb  in  order  that  the 
final  point  may  fall  near  the  center  of  its  top.  In  driving 
a  stake,  the  axeman  should  watch  for  signals.  It  is  better 
to  draw  the  stake  by  a  slanting  blow  than  to  hammer  the 
stake  over  after  it  is  driven.  Good  stake  drivers  are  scarce. 


24  THE  CHAIN  AND  TAPE. 

PROBLEMS  WITH  THE  CHAIN  AND  TAPE. 

General  Statement.— Each  problem  is  stated  under  the 
following  heads: 

(a)  Equipment. — In  which  are  specified  the  articles  and  in- 
struments assigned  or  required  for  the  proper  performance 
of  the  problem.     A  copy  each  of  this  manual  and  of  the 
regulation  field  note  book,  with  a  hard  pencil  to  keep  the 
record,  form  part  of  the  equipment  for  every  problem  as- 
signed. 

(b)  Problem. — In  which  the  problem  is  stated  in  general 
terms.    The  special  assignments  will  be  made  by  program. 

(c)  MethiHlK. — In  which  the  methods  to  be  used  in  the  as- 
signed work  are  described  more  or  less  in  detail.     In  some 
problems  alternative  methods  are  suggested,  and  in  others 
the  student  is  left  to  devise  his  own. 

PROBLEM  Al.  LENGTH  OF  PACE. 

(a)  Equipment. — (No  instrumental  equipment  required.) 

(b)  Problem—  Investigate  the  length  of  pace  as  follows: 
(1)  the  natural  pace;    (2)  an  assumed  pace  of  3  feet;   and 
(3)  the  effect  of  speed  on  the  length  of  the  pace. 

(c)  Method*. — (1)  On  an  assigned  course  of  known  length 
count  the  paces  while  walking  at  the  natural  rate.    Observe 
the  nearest  0.1  pace  in  the  fraction  at  the  end  of  the  course. 
Secure  ten  consecutive  results,  with  no  rejections,  varying 
not  more  than  2  per  cent.     (2)  Repeat  (1)  for  an  assumed 
3-foot  pace.     (3)  Observe  in  duplicate  time  and  paces  for 
four  or  five  rates  from  very  slow  to  very  fast,  with  paces  to 
nearest  0.1  and  time  to  nearest  second.     Record  data  and 
make  reductions  as  in  form  opposite. 

PROBLEM  A2.     DISTANCES  BY  PACING. 

(a)  Equipment.— (No  instrumental  equipment  required.) 

(b)  Problem. — Pace  the  assigned  distances. 

(c)  .VHIifdH.— (1)    Standarize    the   pace   in    duplicate   on 
measured  base.    (2)  Pace  each  line  in  duplicate,  results  dif- 
fering not  more  than  2  per  cent.     Record  and  reduce  as  in 
form. 


PROBLEMS. 


25 


26.         THE  CHAIN  AND  TAPE. 
PROBLEM  A3.   AXEMAN  AND  FLAGMAN  PRACTICE. 

(a)  Equipment. — Flag  pole,  axe,  4  flat  stakes,  1  hub,  tacks. 

(b)  Problem. — Practice  the  correct  routine  duties  of  axe- 
man and  flagman. 

(c)  Method*. — (1)  Number  three  station  stakes  to  indicate 
representative  cases  and  drive  them  properly.     (2)  Drive  a 
hub  flush  with  ground  and  tack  it;  number  a  witness  stake 
and  drive  it  properly.     (3)  Arrange  program  of  signals  with 
partner,  separate  l.OCO  feet  or  so  and  practice  same.     (4) 
Signal  say  five  station   numbers  to  each   other  and   after- 
wards compare   notes.     Make   concise   record   of  the   fore- 
going steps. 

"  PROBLEM   A4.     RANGE  POLE  PRACTICE. 

(a)  Equipment.— 4  flag  poles. 

(b)  Problem. —Given  two  hubs  1.000  feet  or  so  apart,  inter- 
polate a  flag  pole  say  100  feet  from  one  hub,  remove  the  dis- 
tant pole,  prolong  the  line  by  successive  100-foot  sights  and 
note  the  error  at  distant  hub.     Repeat  process  for  200-foot 
and  300-foot  sights. 

(c)  Method*— (1)   Set  distant  flag  pole  precisely  behind 
hub  and  hold  spike  of  pole  on  tack  of  near  hub;   lying  on 
ground  back  of  near  hub,  line  in  pole  100  feet  (paced)  dis- 
tant; remove  pole  from  distant  hub,  and  prolong  by  100 -foot 
sights  up  to  distant  hub,  noting  error  to  nearest  0.01  foot. 
(2)  Repeat  in  reverse  direction,  using  200-foot  sights.     (3) 
Repeat  with  300-foot  sights.     Avoid  all  bias.     Record  data 
in  suitable  form,  describing  steps  concisely. 

PROBLEM  A5.  STANDARDIZING  CHAIN  OR  TAPE. 

(a)  Ei/nipment. — Chain  or  tape  assigned  in  any  problem 
where  standard  length  of  chain  may  be  of  value. 

(b)  Problem. — Determine  the  length  of  the  assigned  chain 
or  tape  by  comparison  with  the  official  standard  under  the 
conditions  of  actual  use. 

(c)  Method*. — In  standardizing  tape,  reproduce  the  condi- 
tions of  actual  use  as  regards  tension,  support,  etc.,  bring 


PROBLEMS.  27 

one  end  graduation  of  chain  or  tape  to  coincide  with  one 
standard  mark,  and  observe  fraction  at  the  other  end  with 
a  scale.  As  a  general  rule,  observe  one  more  decimal  place 
than  is  taken  in  the  actual  chaining. 

PROBLEM  A6.    DISTANCES  WITH  SURVEYORS'  CHAIN. 

(a)  Etiu'tpinetit. — Surveyors'  chain    set  of  chaining  pins,  2 
plumb  bobs,  2  flag  poles,  (unless  instructed    otherwise). 

(b)  PruMnn.—Qn  an  assigned  chaining  course  about  one 
mile  long  measure  distances  with  the  surveyors'  chain  to 
the  nearest  0.1  link,  and  repeat  the  measurements  in  the 
opposite  direction. 

(c)  MrtlHKlx.—d)  Standardarize  the  chain  before  and  after 
as  prescribed  in  A5.     (2)  Chain  along  the  assigned  course, 
noting  the  distances  from  the  starting  point  to  the  several 
intermediate  points  and  to  the  end  station.     Observe  frac- 
tions to  the  nearest  0.1  link  by  estimation.     (3)  Repeat  the 
chaining  in  the  opposite  direction,  noting  the  distances  from 
the  end  point,  as  before.    The  difference  between  the  totals 


•J27 
30 JOt 

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28  THE  CHAIN  AND  TAPE. 

in  the  two  directions  should  not  exceed  1:5,000.  Retain  the 
same  party  organization  throughout  the  problem.  Record 
the  data  as  in  the  prescribed  form. 

PROBLEM  A7.      DISTANCES   WITH    THE    ENGINEERS- 
CHAIN. 

(a)  Equipment.— Engineers'  chain,  set  of  chaining  pins,  2 
plumb  bobs,  2  flag  poles  (unless  instructed  otherwise.) 

(b)  Problem. — On  an  assigned  chaining  course  about  cne 
mile  long  measure  distances  with  the  engineers'  chain  to 
the  nearest  0.1  foot,  and  repeat  the  measurements  in  the  op- 
posite direction. 

(c)  Method*.— (I)  Standardize  the  chain  before  and  after, 
as  prescribed  in  A5.     (2)  Chain  along  the  assigned  course, 
noting  the  distances  from  the  starting  point  to  the  several 
intermediate  points  and  to  the  end  station.     Observe  frac- 
tions to  the  nearest  0.1  foot  by  estimation.     (3)  Repeat  the 
chaining  in  the  opposite  direction,  noting  the  distances  from 
the  end  point,  as  before.    The  difference  between  the  totals 
in  the  two  directions  should  not  exceed  1:5,000.     Retain  the 
same  party  organization  throughout  the  problem.     Record 
the  data  as  in  the  form  opposite. 

PROBLEM    A8.     DISTANCES     WITH     100-FOOT    STEEL 
TAPE. 

(a)  Equipment. — 100-foot  steel  band  tape  with  end  foot 
graduated  to  tenths,  set  of  chaining  pins,  2  plumb  bobs,  2' 
flag  poles,  (unless  instructed  otherwise). 

(b)  Problem. — On  an  assigned  chaining  course  about  one 
mile  long  measure  distances  with  the  100-foot  steel  band 
tape  to  the  nearest  0.01  foot,  and  repeat  the  measurements 
in  the  opposite  direction. 

(c)  Methods. — (1)   Standardize  before  and  after,  as  pre- 
scribed in  A5.     (2)  Chain  along  the  assigned  course,  noting 
the  distances  from  the  starting  point  to  the  several  inter- 
mediate points  and  to  the  end  station.     In  observing  the 
fractions,  first  determine  the  foot  units,  then  estimate  the 
nearest  0.1  foot,  then  shift  the  tape  along  one  foot  and  read 
the  exact  fraction  on  the  end  of  the  tape,  estimating  the 


PROBLEMS. 


100.10 
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t**a 


J£7+.J 

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30.  THE  CHAIN  AND  TAPE. 

nearest  0.01  foot.  (3)  Repeat  the  measurement  in  the  oppo- 
site direction,  noting  the  distances  from  the  end  point,  as 
before.  The  difference  between  the  totals  in  the  two  direc- 
tions should  not  exceed  1:10,000.  Retain  the  same  party 
organization.  Record  data  as  in  form. 

PROBLEM     A9.     HORIZONTAL    DISTANCE    ON    SLOPE 
WITH  STEEL  TAPE. 

(a)  Equipment—  100-foot  steel  tape  with  etched  gradua- 
tions to  0.01  foot,  set  of  chaining  pins,  2  plumb  bobs,  3  flag 
poles,  axe,  supply  of  pegs,  engineers'  level  and  rod,  (unless 
otherwise  instructed). 

(b)  Problem. — Determine  the  horizontal  distance  between 
two  assigned  points  on  a  steep  slope,  (1)  by  direct  horizon- 
tal measurement,  and  (2)  by  measurement  on  the  slope  and 
reduction  to  the  horizontal. 

(c)  Method*.— (I)  Standardize  the  tape  for  each  method, 
as  prescribed  in  A5,  both  before  and  after  the  day's  chain- 
ing.    (2)  In  chaining  down  hill,  rear  c1i<iir>n<in  lines  in  flag 
pole  in  hand  of  head  chainman,  then  holds  tape  end  to  tack 
on  hub;  flnymnn  stands  50  feet  or  more  from  line  opposite 
middle  of  tape  and  directs  head  chainman  in  leveling  front 
end,  then  supports  middle  point  of  tape  under  direction  of 
head   chainman;    liead   cJniirnmn,   with   spring    balance   at- 
tached to  tape  and  using  pole  as  help  to  steady  pull,  brings 
tension  to  12  pounds;  recorder  plumbs  down  front  end,  and 
sets  pin  slanting  sidewise.    After  checking  the  pin,  proceed 
with  the  next  100  feet.     In  chaining  up  hill,  follow  same 
general     method,     using     plumb     bob     at     rear     end.     In 
leveling  the  tape  the  tendency  will  be  to  get  the  down  hill 
end  too  low.    Chain  the  line  in  duplicate,  retaining  the  same 
organization.     (3)  Chain  the  line  again  in  duplicate,  tape 
lying  on  the  ground,  pull  12  pounds,  pins  set  plumb,  frac- 
tion direct  to  nearest  0.01  foot.     Set  temporary  pegs  flush 
with  ground  every  100  feet  and  also  at  intermediate  sudden 
changes  of  slope,  for  levels.    Determine  differences  of  eleva- 
tion between  successive  pegs,  unless  the  leveling  data  are 
supplied  to  the  party.     Record  data  and  make  reductions 
and  comparisons  as  in  form. 


PROBLEMS. 


31 


32  THE  CHAIN  AND  TAPE. 

PROBLEM  A10.  ANGLES  OF  A  TRIANGLE  WITH  TAPE. 

(a)  Equipment.— 100-foot  steel  tape,  50-foot  metallic  tape, 
set  of  chaining  pins,  2  plumb  bobs,  2  flag  poles,  five-place 
tables  of  trigonometric  functions   (each  member  of  party 
to  have  tables). 

(b)  Problem. — Measure  the  angles  of  an  assigned  triangle 
with  the  steel  tape  and  also  with  the  metallic  tape,  the  error 
of  closure  not  to  exceed  3  minutes. 

(c)  ^f('t1i<>(lH.—(l)  Measure  each  angle  with  the  steel  tape 
by  both  the  chord  and  tangent  methods,  100-foot  radius, 
the  difference  in  the  two  results  not  to  exceed  2  minutes. 
If  the  angle  is  near  90°,  the  tangent  method  may  be  applied 
to  the  bisected  angle.     (2)  After  securing  satisfactory  check 
on  an  angle  with  the  steel  tape,  make  a  rapid  but  careful 
measurement  with  the  metallic  tape,  radius  50  feet.     The 
results  may  be  taken  to  the  nearest  half  minute.     (3)  Meas- 
ure at  least  one  angle,  preferably  on  smooth  ground,  by  lay- 
ing out  an  arc  with  radius  of  57.3  feet,  setting  pins  every 
few  feet,  and  measuring  the  actual  arc.    Give  close  attention 
to  alinement  throughout.    Record  data  and  make  reductions 
as  in  form  on  preceding  page. 

PROBLEM  All.  SURVEY  OF  FIELD  WITH  STEEL  TAPE. 

(a)  E<iiiii>iiiciit. — 100-foot  steel  tape,  set  of  chaining  pins, 
2  plumb  bobs,  4  flag  poles,  five-place  table  of  functions. 

(b)  Problem—  Make  survey  of  an  assigned  field  with  tape, 
collecting  all  data  required  for  plotting  the  field  and  calcu- 
lating its  area  by  the  "perpendicular,"   "three-side,"   and 
"angle"  methods. 

(c)  .VetJitMl*.— Standardize  the  tape  once.    (2)  Examine  the 
field  carefully  and  plan  the  survey.     (3)   Measure  the  re- 
quired angles   with  tape.      (4)    Locate  the   perpendiculars. 
(5)   Chain  all  necessary  lines,  and  also  take  distances  to 
feet  of  perpendiculars.    Follow  form. 

PROBLEM  A12.  AREA  OF  FIELD  BY  PERPENDICULAR 
METHOD. 

(a)  E<iitii)i>i<'nt.— Five-place  table  of  logarithms. 

(b)  Problem—  Calculate  the  area  of  the  assigned  field  by 


PROBLEMS 


m 


=  OOOOOHSS63C,  *<. 


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34  THE  CHAIN  AND  TAPE. 

the    perpendicular    method,    using    the    data    collected    in 
Problem  All. 

(c)  Methuds. — (1)  Prepare  form  for  calculation;  transcribe 
data,  and  carefully  verify  transcript.  (2)  Calculate  double 
areas  of  the  several  triangles  by  contracted  multiplication, 
perpendicular  method,  preserving  a  consistent  degree  of 
precision.  (3)  Make  the  same  calculations  with  logarithms, 
as  a  check.  (4)  Combine  the  verified  results,  as  shown  in 
form. 

PROBLEM    A13.     AREA    OF    FIELD    BY     THREE-SIDE 
METHOD. 

(a)  Equipment.— Five-place  table  of  logarithms. 

(b)  Problem. — Calculate  the  area  of  the  assigned  field  by 
the  three-side  method. 

(c)  Mettled*.— (1)    Prepare    form    for    calculation;    tran- 
scribe data,  and  carefully  verify  transcript.     (2)   Calculate 
the  areas  of  the  several  triangles  by  logarithms,  three-side 
method     preserving     proper     units     in     the     results.     (3) 
Carefully  review  the  calculations,  and  combine  the  verified 
results,  as  in  the  form  opposite. 

PROBLEM  A14.  AREA  OF  FIELD  BY  ANGLE  METHOD. 

(a)  Equipment. — Five-place  table  of  logarithms. 

(b)  Problem. — Calculate  the  area  of  the  assigned  field  by 
the  "two  sides  and  included  angle"  method,  using  the  data 
collected  in  All. 

(c)  Me11inds.—  (\)  Prepare  form,  transcribe  data,  and  ver- 
ify copy.     (2)  Calculate  the  double  areas  of  the  several  tri- 
angles by  contracted  multiplication,  angle  method,  preserv- 
ing consistent  accuracy  in  results.     (3)  Make  same  calcula- 
tions by  logarithms,  as  a  check.     (4)  Combine  the  checked 
results.    Follow  the  form  opposite. 

PROBLEM  A15.   AREA   OF  FIELD  FROM   PLAT. 

(a)  Equipment.— Drafting    instruments,    papar.    etc..    pla- 
nimeter,  (as  assigned). 

(b)  PrrMfin.— Determine  the  area  of  the  assigned   field 
directly  from  the  plat. 


PROBLEMS. 


36 


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36  THE  CHAIN  AND  TAPE. 

(c)  Methods.— (I)  Make  an  accurate  plat  of  the  field  from 
the  notes  secured  in  All,  using  a  prescribed  scale.  (2)  De- 
termine the  area  of  the  field  by  resolving  the  polygon  into 
an  equivalent  triangle.  (3)  Determine  the  area  from  the 
plat  by  the  polar  planimeter  and  by  one  of  the  following 
"home-made"  planimeters:  "bird  shot"  planimeter,  "jack 
knife"  planimeter,  cross-section  paper,  parallel  strip,  weigh- 
ing, etc.  (4)  Prepare  on  the  plat  a  tabulated  comparison  of 
results  secured  by  the  several  methods.  (5)  Finish  the  plat, 
as  required. 


PROBLEM  A16.  SURVEY  OF  FIELD  WITH  CURVED 
BOUNDARY. 

(a)  Equipment. — 100-foot  tape,  50-foot  metallic  tape,  set  of 
chaining  pins,  2  plumb  bobs,  4  flag  poles. 

(b)  Problem-. — Make  survey  with  tape  of  an  assigned  tract 
having  a  curved  boundary,  collecting  all  data  required  for 
plotting  the  field  and  calculating  its  area. 

(c)  Methods. — (1)  Standarize  the  tape  once  to  nearest  0.01 
foot.     (2)  Examine  the  tract  carefully  and  plan  the  survey 
so  as  to  secure  a  simple  layout  of  base  lines  designed  to  give 
short  offsets  to  the  curved  boundaries.     (3)  Locate  the  per- 
pendiculars, if  any,  and  chain  all  lines;  on  the  curved  sides, 
take  offsets  so  as  to  secure  a  definite  location,  and  as  a  rule 
take  equal  intervals  on  the  same  line.     Follow  the  form 
opposite. 

PROBLEM     A17.     AREA     OF     FIELD     WITH     CURVED 
BOUNDARY. 

(a)  Equipment. — (No  instrumental  equipment  required). 

(b)  Problem.— Calculate  the  area  of  the  assigned  field  with 
curved  boundary  by  "Simpson's  one-third  rule",  using  the 
data  collected  in  Problem  A16. 

(c)  Methods— (1)  Prepare  form  for  calculation;  transcribe 
data  in  convenient  form  for  calculation,  and  carefully  check 
copy.  (2)  Calculate  the  area  of  the  polygon  formed  by  the 
base  lines,  preferably  by  the  perpendicular  method.     (3) 
Calculate  the  areas  of  the  curved  figures  by  "Simpson's  one- 


PROBLEMS. 


210981 


38  THE  CHAIN  AND  TAPE 

third  rule,"  which  is  as  follows:  "Divide  the  base  line  into 
an  even  number  of  equal  parts  and  erect  ordinates  at  the 
sum  by  one-third  of  the  common  distance  between  ordi- 
nates, twice  the  sum  of  all  the  other  odd  ordinates,  and 
four  times  the  sum  of  all  the  even  ordinates;  multiply  the 
sum  by  one-third  of  the  common  distance  between  ordi 
nates."  The  field  notes  might  have  been  taken  with  special 
reference  to  the  rule,  but  it  is  better  to  take  from  the  notes 
the  largest  even  number  of  equal  segments,  assuming  the  re- 
maining portion  to  be  a  trapezoid  or  triangle.  (4)  Give 
signs  to  the  several  results  by  reference  to  the  field  sketch, 
and  combine  them  algebraically  to  get  the  net  area,  as 
shown  in  the  accompanying  form. 

PROBLEM     A18.     AREA     OF     FIELD     WITH     CURVED 
BOUNDARY  FROM   PLAT. 

(a)  Equipment. — Drafting   instruments,    paper,    etc.,    pla- 
nimeter  (as  assigned). 

(b)  Problem. — Determine  the  area  of  the  field  with  curved 
boundary  directly  from  the  plat. 

(c)  Methods. — (1)  Make  an  accurate  plat  of  the  field  from 
the  notes  obtained  in  A16,  using  a  prescribed  scale.     (2) 
Determine  its  area  directly  from  plat  by  two  methods  men- 
tioned in  (3)  of  A15,  other  than  those  used  in  that  problem. 
(3)  Prepare  on  the  plat  a  tabulated  comparison  oi'  the  re- 
sults by  the  several  methods.     (4)   Finish  the  plat,  as  re- 
quired. 

PROBLEM  A19.   PASSING  AN  OBSTACLE  WITH   TAPE. 

(a)  Equipment. — 100-foot  steel  tape,  set  of  chaining  pins, 
plumb  bobs,  4  flag  poles. 

(b)  Problem. — Prolong  an  assigned   line  through   an   as- 
sumed obstacle  by  one  method  and  prove  by  another,  finally 
checking  on  a  precise  point  previously  established. 

(c)  Methods. — Given  two  hubs,  A  and  B,  200  feet  apart, 
prolong  line  and  establish  C  200  feet  from  B:     (1)  by  con- 
structing a  200-foot  square  in  one  direction;  and  (2)  by  lay- 
ing off  a  200-foot  equilateral  triangle  on  the  opposite  side, 
using  pins  to  mark  points  thus  established.     (3)  Prolong  the 


PROBLEMS. 


e/Ktea  point    C  rX'Oj*   from  A  ana  B, 

G  ,  ff.,   and  6/Jtcted  CA  of  O    and  C3  at 
£.  Caainea  OE.    Tnen    calculated  AS 


ot.rt/a/  meaj'/nt 


40  THE  CHAIN  AND  TAPE 

line  by  each  method  to  the  hub  D,  200  feet  from  C,  and 
record  discrepancies  in  line.  (4)  Interpolate  a  point  at  C 
on  tme  line  between  B  and  D,  and  note  errors  of  prolonga- 
tion at  C.  Record  as  in  form. 

PROBLEM  A20.  OBSTRUCTED  DISTANCE  WITH  TAPE. 

(a)  Equipment. — 100-foot  steel  tape,  set  of  chaining  pins, 
2  plumb  bobs,  4  flag  poles. 

(b)  Problem.— Determine   the   distance  between   two   as- 
signed   points  through  an  assumed  obstruction  to  both  vis- 
ion and  measurement,  using  two  independent  methods,  and 
finally  chaining  the  actual  distance. 

(c)  Methods. — (1)    Standardize  the  tape.     (2)    Determine 
the  distance  between  the  assigned  points  by  constructing  a 
line  parallel   to   the  given   line,   and   equal   or   bearing   a 
known  relation  to  it.    (3)  Secure  a  second  result  by  running 
a  random  line  from  one  hub  past  the  other  so  that  a  per- 
pendicular less  than  100  feet  long  may  be  let  fall,  measur- 
ing the  two  sides  and  calculating  the   hypothenuse.     (4) 
After   securing   two   results    differing   by   not   more    than 
1:1,000,  chain  the  actual  distance.    Follow  form. 

PROBLEM  A21.  RUNNING  IN  CURVE  WITH  TAPE. 

(a)  Equipment.— 100-foot  steel  tape,  50-foot  metallic  tape, 
set  of  chaining  pins,  2  plumb  bobs,  3  hubs,  6  flat  stakes, 
marking  crayon,  tacks,  five-place  table  of  functions. 

(b)  Problem. — Lay    out  two    lines    making    an    assigned 
angle  with  each  other,  and  connect  them  with  a  prescribed 
curve  by  the  "chord  offset"  method. 

(c)  Methods.— (1)  Calculate  the  radius,  R,  for  the  given 
degree  of  curve,  D.  (2)  Calculate  the  tangent  distance,  T,  for 
the  given  radius,  R,  and  angle  of  intersection,  I.     (3)  Calcu- 
late the  chord  offset,  d,  and  tangent  offset,  t,  for  the  known 
radius,  R,  chord,  c  and  degree,  D.     (4)  At  the  given  point 
intersection   (P.  I.),  A,  lay  off  the  given  angle,  /,  by  the 
chord  method.     (5)  From  the  P.  I.  lay  off  T  along  the  two 
tangent  lines  and  locate  point  tangent  (P.  T.)   and  point 
curve  (P.  C.),  setting  hubs  at  P.  C.  and  P.  T.,  with  guard 
stake  at  each  hub.     (6)  Run  in  the  curve,  by  chord  offsets, 


PROBLEMS. 


41 


LOCATION     OF    CURVE 
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42  THE  CHAIN  AND  TAPE. 

beginning  at  P.  C.  and  checking  at  P.  T.  Calling  P.  C. 
Station  0,  establish  Station  1  by  laying  off  tangent  offset,  t, 
and  chord,  c.  Having  one  station  on  the  curve,  the  next  is 
located  by  prolonging  the  chord  and  forming  an  isosceles 
triangle  having  the  chord  offset  as  a  base.  Check  on  the 
P.  T.,  noting  the  discrepancy  of  distance  and  line.  Also 
establish  the  tangent  again  by  tangent  offset  and  observe 
the  error  of  line.  Follow  form. 

PROBLEM  A22.  DISCUSSION  OF  ERRORS  OF  CHAINING. 

(a)  Equipment. — (No  instrumental  equipment,  unless 
further  data  are  desired,  in  which  case  Problems  A6,  A7  and 
A8  may  be  assigned  again). 

(bj    Problem. — Investigate  the  errors  of  linear   measure- 
ment with   the  several  kinds  of  chains  and  tape,  with  the 
view  to  determine  practical  working  tests  or  coefficients 
of  precision  for  actual  use. 

(c)  Methods.— Assume  that  the  conditions  in  Problems 
A6,  A7  and  A8  are  practically  constant  in  the  same  problem, 
and  that  the  actual  differences  between  observed  lengths 
of  the  several  segments  when  chained  in  opposite  direc- 
tions, represent  the  normal  errors  with  the  particular  chain 
and  chainmen;  then  tabulate:  (1)  the  measured  lengths  of  all 
rossible  segments  of  the  chaining  course,  either  from  direct 
observation  or  by  subtraction;  (2)  the  actual  errors  or  dif- 
ferences between  the  two  results,  giving  signs;  (3)  the 
chaining  ratios,  l:d,  and  the  decimal  expressions  of  the 
same  to  six  places;  (4)  the  "coefficients  of  precision"  for 
each  case,  calculated  by  formula,  or  more  quickly,  taken 
from  the  diagram  in  the  chapter  on  errors  of  surveying;  (5) 
the  mean  decimal  chaining  ratio  and  its  equivalent;  and  (6) 
the  mean  coefficient  of  precision.  Follow  the  prescribed 
form. 

PROBLEM  A23.  TESTING  (OR  ESTABLISHING)  AN  OF- 
FICIAL STANDARD  OF  LENGTH. 

(a)  Equipment.— Standard  tape  (with  certified  length 
given),  turnbuckle  adjustments  with  bolts,  spring  balance, 
standard  steel  rule  graduated  to  0.01  inch,  2  thermometers, 


PROBLEMS. 


2  microscopes,  strips  of  wood,  a  watch. 

(b)  P roll f HI—  Make  a  series  of  ten  observations  with  a 
standardized  steel  tape  for  the  purpose  of  testing  (or  estab- 
lishing) an  official  standard  of  length,  observing  the  near- 
est 0.0001  foot. 

(c)  UetJtods. — (If  a  neir  offical  standard  is   being  estab- 
lished, one  standard  mark  may  be  made  permanent,  and  the 
precise  distance  taken  to  an  approximate  temporary  point 
on  the  other  bolt,  the  exact  correction  being  applied  after 
a  sufficient  number  of  results  have  been  obtained.     If  the 
sun  is  shining,  the  tape  should  be  protected  by  a  wooden 
box  or  other  covering  throughout  its  length.     Cloudy  days 
or  night  time  give  best  results.    The  observations  should  be 
made  briskly  so  as  to  have  slight  range  of  temperature. 
If  isolated  standard  monuments  are  used,  their  foundation 
should  go  below  frost  line,  and  the  monuments  should  be 
located  so  as  to  suffer  as  little  as  possible  from  heaving.    If 
the  standard   marks   are   indoors,    the  conditions   are   less 
difficult  to  control). 

(1)  Arrange  "bucksaw"  or  turnbuckle  adjustments,  each 
held  firmly  by  a  bolt  dropped  into  a  piece  of  gaspipe  driven 


44  THE  CHAIN  AND  TAPE. 

flush  with  surface  of  ground,  with  spring  balance  and  tape 
lined  up,  as  shown  in  sketch  in  accompanying  form;  place 
the  two  thermometers  at  the  one-third  points  as  nearly  as 
possible  under  the  actual  conditions  of  the  tape.  (2)  With 
four  men  in  party,  No.  1  sets  end  graduation  precisely  at 
one  standard  mark  by  means  of  screw  adjustments  and  mi- 
croscope; No.  2  sets  balance  at  12  pounds;  No.  3  obseives 
fraction  at  other  standard  mark  by  means  of  steel  scale 
graduated  to  0.01  inch,  estimating  to  nearest  0.001  inch  (say 
0.0001  foot)  by  microscope;  and  No.  4  records  all  data,  ob- 
serves time  to  nearest  minute,  and  temperature  to  nearest 
0.1  degree.  Nos.  1,  2  and  3  should  lie  flat.  Release  the  ten- 
sion between  observations.  Record  and  reduce  as  in  form. 

PROBLEM  A24.  DETERMINATION  OF  CONSTANTS  OF 
A  STEEL  TAPE. 

(a)  Equipment. — Steel  tape  and  other  articles  named  in 
preceding  problem. 

(b)  Problem. — Determine  coefficients    of    expansion    and 
stretch  of  the  assigned  tape. 

(c)  Metliods.^(To  be  devised  by  the  student.) 

PROBLEM  A25.     COMPARISON  OF  DIFFERENT  MAKES 
AND  TYPES  OF  CHAINS  AND  TAPES. 

(a)  Equipment. — Department  equipment  and  collection  of 
catalogs  of  representative  instrument  makers. 

(b)  Problem. — Make  a  critical  comparison  of  the  several 
types  of  chains  and  tapes  made  by  different  makers. 

(c)  Methods. — Study  the  different  catalogs  and  prepare  a 
systematic  and  concise  report. 


CHAPTER  III. 
THE  COMPASS. 


Description. — The  magnetic  compass  consists  of  a  line  of 
sight  attached  to  a  graduated  circular  box,  at  the  center  of 
which  is  a  magnetic  needle  supported  on  a  steel  pivot.  The 
compass  box  is  attached  to  a  tripod  or  Jacob  staff  by  a  ball 
and  socket  joint,  and  is  leveled  by  means  of  the  plate  levels. 
The  needle  should  be  strongly  magnetized  and  have  an 
agate  cap  to  receive  the  point  of  the  hardened  steel  pivot. 
The  dip  of  the  needle  is  counter-balanced  by  a  small  coil  of 
wire,  which  can  be  shifted  as  desired.  The  E  and  W  points 
are  reversed. 

In  Fig.  10  are  shown  the  usual  types  of  magnetic  com- 
passes: (a)  the  vernier  compass;  (b)  the  plain  compass;  (c) 
the  vernier  pocket  compass  with  folding  sights;  (d)  the 
ordinary  pocket  compass;  (e)  the  prismatic  compass. 


Fig.  10. 


46  THE  COMPASS. 

Declination  of  the  Needle.— If  the  needle  is  allowed  to 
swing  freely,  its  magnetic  axis  will  come  to  rest  in  the 
magnetic  meridian.  The  horizontal  angle  between  the  mag- 
netic meridian  and  the  true  meridian  at  any  point  is  called 
the  magnetic  declination  for  that  point.  Imaginary  lines 
joining  points  on  the  earth's  surface  having  the  same 
declination  are  called  isoyonic  lines.  The  isogonic  line  join- 
ing the  points  of  zero  declination  is  called  the  (ninnic  line. 
Fig.  12  is  an  isogonic  chart  of  the  entire  earth's  surface.  Of 
the  three  isogonic  lines,  one  passes  through  Michigan, 
Ohio,  etc. 


Diagram  of  Secular  Variation  of  the 
MAGNETIC    DECLINATION  IN    UNITED  STATES. 


Diagram  or 

DAILY      VARIATION 

of  the 
MAGNETIC 

DECLINATION, 
Northern  United  States 


DECLINATION  OF  THE  NEEDLE. 


47 


Variation  of  the  Declination.—  The  declination  of  the 
needle  is  not  a  constant  at  any  place.  The  change  or 
fluctuation  is  called  the  rarkitiun  of  the  declination.  The 
variations  of  the  magnetic  needle  are  of  several  kinds: 
secular,  daily,  annual,  lunar,  and  irregular  variations  due  to 
magnetic  storms.  The  most  important  of  these  is  the 
secular  variation  which  is  illustrated  in  the  uppsr  diagram 


48 


THE  COMPASS. 


of  Fig.  11  for  a  series  of  representative  points  in  the  United 
States.  This  diagram  shows  that  the  extreme  range  or 
swing  of  the  needle  is  roughly  6°  or  T ,  and  that  the  period 
of  time  between  extreme  positions  is  about  a  century  and  a 
half.  Also  that  the  wave  of  magnetic  influence  progresses 
across  the  continent  alike  in  successive  cycles.  At  present 
(1900)  the  needle  is  at  its  extreme  western  position  at  East- 
port,  Me.,  and  at  its  extreme  eastern  pointing  at  San  Diego, 
Cal.  The  3"  East  isogonic  line  now  passes  through  western 
Indiana,  and  is  moving  westward  at  the  rate  of  about  4' 
per  year.  This  rate  of  change  is  general  throughout  the 
central  part  of  the  United  States,  and  is  represented  by  the 
straight  sections  of  the  curve  in  the  upper  diagram  of 
Fig.  11. 

The  daily  variation  of  the  magnetic  declination  is  shown 
graphically  in  the  lower  part  of  Fig.  11,  the  scale  being 
greatly  magnified  laterally.  It  is  seen  that  the  needle  un- 
dergoes each  day  a  vibration  similar  in  a  general  way  to  the 
grand  swing  of  three  centuries  or  so  shown  in  the  upper 
diagram.  The  magnitude  of  the  daily  movement  in  north- 
ern United  States  ranges  from  5'  in  winter  to  neany  12' 
in  summer  time.  The  needle  is  in  its  mean  daily  position 
between  10  and  11  a.  m.  for  all  seasons.  The  diagram  rep- 
resents the  normal  magnetic  day,  of  which  there  are  per- 
haps five  or  six  per  month. 

Local  Attraction. — The  pointing  of  the  needle  is  af- 
fected by  the  close  proximity  of  magnetic  substances,  such 


Fig.  13. 


USE  OF  THE  COMPASS.  49 

as  iron  ore,  wire  fences,  railroad  rails,  etc.  However,  local 
attraction  does  not  prevent  correct  work,  provided  back 
and  fore  sights  are  taken  without  change  of  magnetic  condi- 
tions. It  is  therefore  especially  important  to  avoid  disturb- 
ances of  the  needle  by  the  chain,  axe,  passing  vehicles,  elec- 
tric wires,  etc.,  or  by  articles  on  the  person  of  the  observer, 
such  as  keys,  knife,  spectacle  frame,  wire  in  the  hat  rim, 
reading  glass  case,  etc.  Also  the  glass  cover  may  become 
electrified  by  friction  and  attract  the  needle,  in  which  case 
it  may  be  discharged  with  the  moistened  finger,  or  by 
breathing  on  it. 

The  Vernier.— The  vernier  is.  an  auxiliary  scale  used 
to  read  fractional  parts  of  the  divisions  of  the  main  scale  or 
1'mb  .  Verniers  are  retrograde  or  direct,  according  as  the 
divisions  on  the  vernier  are  larger  or  smaller  than  those  on 
the  limb.  The  vernier  used  on  compasses  for  the  setting  off 
of  the  declination  is  direct,  and  is  usually  of  the  type  shown 
in  (c)  of  Fig.  13.  In  reading  a  vernier  of  any  kind,  blunders 
may  be  avoided  by  first  estimating  the  fraction  by  eye  be- 
fore noting  the  matched  lines  on  the  two  scales. 

USE- OF  THE  COMPASS. 

Use. — The  compass  is  used:  (1)  to  determine  the  bear- 
ings of  lines;  (2)  to  measure  the  angle  formed  by  two  lines; 
(3)  to  retrace  old  lines.  The  bearing  of  a  line  is  the  hori- 
zontal angle  between  the  line  and  a  meridian  through  one 
end  of  it.  Bearings  are  measured  from  the  north  or  south 
point  90°  each  way.  The  angle  between  two  lines  is  th* 
difference  in  their  directions  as  indicated  by  the  bearings 
Having  the  true  bearings  of  one  side  of  a  polygon,  the  tru«, 
1. tarings  of  the  others  may  be  obtained  by  algebraic  addi- 
t'on  of  the  angles;  or  by  using  the  declination  vernier  so  a# 
lo  read  the  true  bearing  direct  on  the  fore  sights. 

Practical  Hints. — Point  the  north  end  of  the  compass 
box  along  the  line  and  read  the  north  end  of  the  needle. 
Protect  the  pivot  from  needless  wear  by  turning  the  needle 
in  about  the  proper  direction  before  releasing  it.  Always 
lift  the  needle  before  disturbing  the  compass.  Habitually 
obtain  duplicate  needle  readings  on  each  sighting.  Read 
the  needle  by  estimation  to  the  nearest  five  minutes,  that 
is,  to  the  one-sixth  part  of  one-half  degree,  which  is  the 


CO  THE  COMPASS. 

usual  subdivision  of  the  compass  box.  Care  should  be  taken 
to  avoid  parallax  in  reading  the  needle. 

ADJUSTMENTS  AND  TESTS. 

Elementary  Lines.— The  elem<"ntarn  lines  of  the  compass, 
shown  in  (a)  of  Fig.  10,  are:  (1)  the  line  of  sight;  (2)  the 
vertical  axis;  (3)  the  plate  level  lines. 

The  maker  should  see:  (1)  that  the  needle  is  strongly 
magnetized;  (2)  that  the  magnetic  axis  corresponds  with 
the  line  joining  the  two  ends;  (3)  that  the  metal  in  the  com- 
pass box  is  non-magnetic;  (4)  that  the  line  of  sights  passes 
through  the  center  of  graduation;  (5)  that  the  plates  are 
perpendicular  to  the  vertical  axis;  (6)  that  the  zero  of  the 
vernier  coincides  with  the  line  of  sights. 

The  needle  may  be  magnetized  with  a  bar  magnet  or  by 
putting  it  into  the  magnetic  field  of  a  dynamo.  The  metal 
of  the  compass  box  may  be  tested  by  reading  the  needle, 
then  moving  the  vernier  and  noting  if  the  needle  has  moved 
the  same  amount,  this  process  being  repeated  at.  intervals 
around  the  full  circle. 

The  Principle  of  Reversion.— In  adjusting  surveying 
instruments,  the  presence,  direction 'and  amount  of  the  er- 
ror are  made  evident  by  the  method  of  rcrerfionx  which 
doubles  the  apparent  error.  If  there  is  no  difference  after 
reversion,  there  is  no  error. 

Plate  Levels. — To  make  the  plane  of  flic  plate  lerel  line* 
Iterpemlieiilar  to  tlte  vertical  axis. — Level  up  the  instrument 
by  means  of  the  plate  levels  and  reverse  the  compass  box 
in  azimuth,  that  is,  turn  it  through  a  horizontal  angle  of 
180°.  Correct  one-half  the  error,  if  any,  by  means  of  the 
adjusting  screws  at  the  end  of  the  level  tube,  and  bring  the 
bubble  to  the  center  by  the  ball  and  socket  joint.  The  rea- 
sons for  this  process  are  shown  in  (a)  of  Fig.  13. 

Sights.— To  make  the.  plane  of  sigJits  normal  to  tin-  pl<nie  of 
the  plate  level  lines. — With  one  sight  removed  and  the  instru- 
ment leveled,  range  in  with  the  remaining  sight  two  points 
as  far  apart  vertically  as  possible,  say  on  the  side  of  a  build- - 
ing.  Reverse  in  azimuth  and  bring  the  bottom  of  the  sight 
in  range  with  the  lower  point;  if  the  upper  point  is  then  in 
range,  the  sight  is  in  adjustment.  If  not,  correct  one-half 
the  error  by  putting  paper  under  one  side,  or  by  filing  off 
the  other  side.  Repeat  process  for  the  other  sight. 


PROBLEMS.  51 

The  Pivot. — To  mljuxt  tlie  pivot  to  the  center  of  ilic  i/railn- 
uteiJ  circle— Set  the  south  end  of  the  needle  to  read  zero,  and 
read  the  north  end  of  the  needle;  reverse  the  compass  box 
in  azimuth,  repeat  the  observations,  and  correct  one -half 
the  difference  between  the  two  readings  of  the  north  end 
of  the  needle  by  bending  the  pivot,  using  the  special  wrench 
for  the  purpose.  Turn  the  compass  box  90°  and  repeat. 
See  (b),  Fig.  13. 

The  Needle.— To  *lr«ii/hten  the  needle.— Having  adjusted 
the  pivot,  set  the  north  end  of  the  needle  to  read  zero  and 
bend  the  needle  so  that  the  south  end  reads  zero  also.  Turn 
the  compass  box  and  test  for  other  graduations. 


PROBLEMS  WITH  THE  COMPASS. 


PROBLEM    Bl. 


DECLINATION    OF    THE    MAGNETIC 
NEEDLE. 


(a)  Equipment. — Surveyors'    compass,    flag    pole,    reading 


V L 


WITH       SURVE 
Mr*  f«r/ry  C**,f 


.V..    **-r     oit 


=<S'     COMPA< 
I  A'a  2O  (Atttctt 


52  THE  COMPASS. 

(b)  Problem.— At  a  point  on  the  true  meridian  determine 
the  mean  magnetic  declination  with  the  surveyors'  compass. 

(c)  Methods. —  (1)  Set  the  compass  over  one  point  and  a 
flag  pole  at  another  on  the  true  meridian.     (2)  Lower  the 
needle  and  sight  at  the  flag  pole  carefully  with  the  north 
end  of  the  compass  box  to  the  front.     (3)  When  the  vibra- 
tions of  the  needle  have  ceased,  move  the  vernier  by  means 
of  the  tangent  screw  so  that  the  north  end  of  the  needle 
reads  zero,  and  check  the  sighting  of  the  compass.     (4) 
Read  the  declination  on  the  vernier  to  the  nearest  minute. 
(5)  Lift  the  needle,  verify  the  zero  needle  reading  and  the 
sighting,  read  the  vernier  and  record;   repeat  the  process 
until  ten  satisfactory  consecutive  values  of  tl  ?  declination 
are  obtained.    Observe  the  time  of  each  reading  xo  the  near- 
est minute.     (6)   Correct  the  mean  of  the  ten  values  for 
daily  variation  by  reference  to  the  diagram,  Fig.  11,  using 
the  mean  time.     Record  and  reduce  the  data  as  in  form. 
(Note  that  the  values  in  the  form  were  obtained  by  estimat- 
ing the  nearest  five  minutes.    Which  is  better?     Try  both 
if  time  allows.) 

PROBLEM  B2.  ANGLES  OF  TRIANGLE  WITH  COMPASS. 

(a)  Equipment. — Surveyors'  compass,  two  flag  poles,  read- 
ing glass. 

(b)  Problem. — Measure  the  angles  of  a  given  triangle  with 
the  surveyors'  compass. 

(c)  Methods—  (1)  Set  the  compass  over  one  of  the  vertices 
of  the  triangle  and  a  flag  pole  behind  each  of  the  other  two. 
(2)  Lower  the  needle  and  sight  at  one  of  the  flag  poles  care- 
fully, with  the  north  end  of  the  box  to  the  front.    (3)  When 
the  vibrations  have  ceased,  read  the  north  end  of  the  needle 
to  the  nearest  five  minutes  by  estimation.     (4)    Lift  the 
needle,  verify  the  sighting  and  also  the  reading.     (5)  Turn 
the  compass  box  to  the  other  point  and  determine  the  bear- 
'ing,  as  before.    The  required  angle  is  the  difference  between 
the  two  bearings.    (6)  Measure  the  other  two  angles  in  like 
manner.    The  error  of  closure  must  not  exceed  5  minutes. 
vollow  the  prescribed  form. 


PROBLEMS. 


f 

.Station 


e.*;.^ 

•S'-KC 


WITH     SURVE 


S4  THE  COMPASS. 

PROBLEM  B3.    TRAVERSE  OF  FIELD  WITH  COMPASS. 

(a)  Equipment.— Surveyors'  compass,  2  flag  poles,  engi- 
neers' chain,  set  of  chaining  pins. 

(b)  Problem.— Determine  the  bearings  of  the  sides  of  an 
assigned  field  with  the  surveyors'  compass  and  measure  the 
lengths  of  the  sides  with  an  engineers'  chain. 

(c)  .Vrt/iorf*.— (1)  Set  the  compass  over  one  of  the  corners 
of  the  field  which  is  free  from  local  attraction,  and  set  off 
the  declination  with  the  vernier.   '(2)  Take  back  sight  on 
the  last  point  to  the  left  and  fere  sight  to  the  next  point 
to  the  right,  following  the  methods  used  in  Problem  B2. 
(3)   Repeat  this  process  for  the  remaining  corners  of  the 
polygon  taken  in  succession  to  the  right.     (4)   Chain  the 
sides  of  the  field  to  the  nearest  0.1  foot  by  estimation.     (5) 
Compare  the  chain  with  standard.     (6)  From  the  observed 
bearings  compute  the  interior  angles  of  the  field,  and  the 
true  bearings  of  the  sides.     The  angular  error  of  closure 
must  not  exceed  10  minutes  for  a  five-sided  fielrt  .  Record 
and  reduce  data  as  in  prescribed  form. 

PROBLEM  B4.    AREA  OF  FIELD  WITH  COMPASS. 

(a)  Equipment.— Five-place  table  of  logarithms. 

(b)  Problem.— Compute  the  ar^a  of  the  assigned  field  by 
means  of  latitudes  and  departures. 

(c)  Methods. — (1)    Prepare   forms   for   calculation;    tran- 
scribe data,  and  carefully  verify  copy.     (2)  Compute  lati- 
tudes and  departures  by  contracted  multiplication,  preserv- 
ing results  to  the  nearest  0.1  foot.     (3)  Make  the  same  cal- 
culations by  logarithms,  as  a  check.     (4)  Determine  the  ac- 
tual linear  error  of  closure.     (5)  Determine  the  permissible 
error  of  closure  (see  chapter  on  errors  of  surveying).     (6) 
If  consistent,  distribute  the  errors  in  proportion  to  the  sev- 
eral latitudes  and   departures,  respectively,   repeating  the 
additions  as  a  check.     (7)   Transcribe  field  notes  and  ad- 
justed latitudes  and  departures,  and  verify  transcript.     (8) 
Calculate  the  meridian  distances  of  the  several  stations  and 
lines.     (9)  Calculate  the  latitude  coordinates.     (10)  Calcu- 
late the  partial  trapezoidal  areas  by  multiplying  the  meri- 
dian distances  of  the  lines  by  the  respective  latitudes,  pre- 


PROBLEMS. 


56  THE  COMPASS. 

serving  consistent  accuracy,  and  observing  algebraic  signs. 
(11)  Determine  the  area  by  taking  the  algebraic  sum  of  the 
partial  areas.  Reduce  to  acres,  and  correct  for  standard. 
Follow  the  prescribed  form. 

PROBLEM  B5.     ADJUSTMENT  OF  THE  COMPASS. 

(a)  Equipment— Surveyors'  compass,  adjusting  pin,  small 
screw  driver. 

(b)  Problem.— Make  the  necessary  tests  and  adjustments 
of  the  surveyors'  compass. 

(c)  Methods. — Observe  the  following  program:      (1)    test 
the  magnetism  of  the  needle;  (2)  test  the  metal  of  the  com- 
pass box;   (3)  test  and  adjust  the  plate  levels;   (4)  test  the 
sights;   (5)  test  the  pivot;   (6)  test  the  needle. 

PROBLEM  B6.     COMPARISON  OF  DIFFERENT  MAKES 
AND  TYPES  OF  COMPASSES. 

(a)  Equipment. — Department  equipment,  catalogs  of  rep- 
resentative makers  of  compasses. 

(b)  Problem.— Make  a  critical  comparison  of  the  several 
types  of  compasses. 

(c)  Methods. — Examine    the    department    equipment    and 
study  the  several  catalogs  carefully,  noting  the  character- 
istic features,  prices,  etc.     The  following  items,    at    least, 
should  be  included  in  the  tabulated  report:  name  of  instru- 
ment, length  of  needle,  length  of  alidade,  vernier,  tripod, 
weight,  price,  etc. 


CHAPTER  IV. 
THE  LEVEL. 


Description. — The  engineers'  level  consists  of  a  line  of 
sight  attached  to  a  bubble  vial  and  a  vertical  axis.  Two 
types  of  level,  the  wye  and  dumpy,  Fig.  14,  are  used  by  engi- 
neers. In  the  former  the  telescope  rests  in  Y-shaped  sup- 
ports, from  which  it  may  be  removed.  In  the  dumpy  level 
the  telescope  is  fixed.  The  dumpy  is  a  favorite  with  British 
engineers  and  the  wye  level  with  Americans.  The  two  types 
differ  chiefly  in  the  methods  of  adjustment.  A  third  type, 
not  shown  in  the  cuts,  is  called  the  level  of  precision  be- 
cause of  its  use  solely  for  work  of  extreme  refinement. 


DUMPY    LEVEL. 

Fig.   14. 


58 


THE  LEVEL, 


In  Fig.  15  are  shown:  (a)  an  architects'  or  builders'  level 
of  the  wye  type;  (b)  a  roadbuilders  level  of  the  dumpy 
type;  (c)  a  reconnaissance  level  with  a  decimal  scale  for 
reading  horizontal  distances  direct;  (d)  a  water  level  some- 
times used  in  locating  contours;  (e)  a  Locke  hand  level;  (f) 
a  clinometer;  (g)  a  binocular  hand  level. 


Fig.  15. 
THE  TELESCOPE. 

Principles.— The  telescope  used  in  the  engineers'  level 
and  transit,  shown  in  section  in  Fig.  16  and  22,  consists 
of  an  objective  or  object  glass  which  collects  the  light  and 
forms  an  image  in  the  plane  of  the  cross-hairs,  and  an  ocular 
or  eyepiece  which  magnifies  the  image  and  cross-hairs.  The 
cross-hairs  are  thus  at  the  common  focus  of  the  objective 
and  eyepiece.  The  principle  of  this  type  of  telescope,  both 
optically  and  mechanically,  may  be  illustrated  by  the  photo- 
graphic camera  if  cross  lines  be  ruled  on  the  ground  giass 
focusing  plate  and  a  microscope  be  used  in  viewing  the 
image  formed  by  the  lens.  Telescopes  of  the  above  class  are 
called  measuring  telescopes,  while  those  of  the  opera  glass 
type  are  termed  seeing  telescopes.  The  latter  have  no  real 
image  formed  between  the  object  glass  and  eyepiece. 

Line  of  Collimation.— The  telescope  of  the  level  or  tran- 
sit may  be  represented  by  a  line,  called  the  line  of  coUiiua- 
tion,  which  joins  the  optical  center  of  the  objective  and  the 


THE  TELESCOPE. 


Mfft.f£-j 

Jo/e.  Tavgeni-_  Li_ne_oj 


•  —  -  -  -*  M&ay^rvjK  —  -_-  -  -  (-Say  4OO') -7! 

»<  2nd  Method. 

Two -Peg   Test. 

Fig.    16. 


60  THE  LEVEL. 

intersection  of  the  cross-hairs.  The  optical  center  is  a  point 
such  that  a  ray  of  light  passing  through  it  emerges  from 
the  lens  parallel  to  its  original  direction.  The  line  of  colli- 
mation  is  independent  of  the  eyepiece. 

Objective. — The  objective  is  a  double  convex  or  plano- 
convex lens.  In  all  good  telescopes  the  objective  is  com- 
pound, that  is,  made  up  of  two  lenses,  with  the  view  to  cor- 
rect two  serious  optical  defects  to  which  a  simple  lens  is 
subject.  These  defects  are  called  chromatic  aberration  end 
spherical  aberration. 

Chromatic  aberration'  is  the  separation  by  the  objective  of 
white  light  into  its  component  colors.  A  lens  which  is  free 
from  this  defect  is  called  achromatic.  A  telescope  is  tested 
for  the  chromatic  defect  by  focusing  on  a  bright  obj  ^ct,  such 
as  a  piece  of  paper  with  the  sun  shining  on  it,  and  noting 
the  colors  on  the  edge  of  the  object  and  especially  at  the 
edge  of  the  field  of  view  as  the  focus  is  slightly  deranged. 
Yellow  and  purple  are  the  characteristic  colors  indicating 
good  qualities  in  the  lens. 

Spherical  aberration  is  a  defect  which  prevails  to  a  serious 
extent  in  a  simple  lens  having  spherical  surfaces.  It  is  due 
to  a  difference  in  the  focal  distance  for  different  concentric 
or  annular  spaces  of  the  objective,  so  that  the  plane  of  focus 
for  rays  passing  through  the  outer  edges  of  the  lens  is  dif- 
ferent from  that  of  the  middle  portion.  A  telescope  is  test- 
ed for  this  defect  by  focusing  on  a  well  defined  object,  such 
as  a  printed  page,  with  the  rays  of  light  cut  off  alternately 
from  the  middle  and  the  edge  of  the  lens.  This  is  best  done 
by  means  of  a  circular  piece  of  paper  with  a  small  round 
hole  in  it. 

As  a  rule,  the  object  glass  in  good  levels  and  transits  con- 
sists of  a  double  convex  lens  of  crown  glass  fitted  to  a  con- 
cavo-convex or  a  plano-concave  lens  of  flint  glass,  the 
former  to  the  front.  The  defects  described  above  are  avoid- 
ed through  the  different  dispersive  and  refractive  powers  of 
the  two  kinds  of  glass,  and  by  grinding  the  surfaces  of  the 
two  lenses  to  the  proper  curvatures. 

Eyepiece. — As  in  the  camera,  the  image  formed  by  the 
objective  is  inverted,  so  that  if  a  simple  microscope  be  used 
as  an  eyepiece,  the  observer  sees  objects  inverted.  Such 


THE  TELESCOPE.  61 

an  eyepiece  Is  commonly  used  on  the  dumpy  level,  as  shown 
in  Pig.  14.  This  form  of  eyepiece  consists  of  two  plano- 
convex lenses  with  their  convex  sides  facing  each  other. 
The  form  of  eyepiece  most  used  in  American  instruments  is 
the  erecting  eyepiece  in  which  two  plano-convex  lenses  re- 
place each  of  the  two  in  the  simpler  form.  The  erecting 
eyepiece  is  much  longer  than  the  simple  one,  as  may  be 
seen  at  a  glance  in  Fig.  14.  While  the  simple  eyepiece  causes 
a  little  confusion  at  first,  owing  to  the  inversion  of  objects, 
it  is  much  superior  to  the  erecting  eyepiece  in  the  matter  of 
clearness  and  illumination. 

The  chief  inherent  defect  in  the  eyepiece  is  a  lack  of 
flatness  of  the  field.  A  single  lens  usually  causes  a  distor- 
tion or  curving  of  straight  lines  in  the  image,  especially  to- 
wards the  edge  of  the  field.  A  telescope  is  tested  for  this 
defect  by  observing  a  series  of  parallel  right  lines,  prefer- 
ably a  series  of  concentric  squares,  which  fill  the  entire  field 
of  view. 

In  the  best  achromatic  eyepieces,  one  or  more  of  the  sep- 
arate lenses  may  be  compounded,  the  curvatures  being  such 
as  to  eliminate  the  color  defect  and  give  rectilinear  qualities 
to  the  lens  or  combination  of  lenses. 

Definition.— The  definition  of  a  telescope  depend®  upon 
the  finish  and  also  the  accuracy  of  the  grinding  of  the 
curved  surfaces  of  the  lenses.  It  may  be  tested  by  reading 
the  time  on  a  watch  or  a  finely  printed  page  at  some  dis- 
tance from  the  instrument. 

Illumination.— Illumination  and  definition  are  apt  to 
be  confused.  Poor  definition  causes  indefinite  details,  while 
poor  illumination  causes  faintness  in  the  image.  The  latter 
may  be  tested  about  dusk,  or  in  a  room  which  can  be  grad- 
ually darkened,  and  can  be  best  appreciated  if  two  telescopes 
of  different  illuminating  qualities  be  compared. 

Aperture  of  Objective. — The  aperture  or  effective  di- 
ameter of  the  objective  is  determined  by  moving  the  end  of 
a  pencil  slowly  into  the  field  and  noting  the  point  where  it 
first  appears  to  the  eye  when  held  say  8  or  10  inches  back 
from  the  eyepiece.  The  process  should  be  repeated  in  the 
reverse  order.  The  annular  space  is  deducted  from  the 
actual  diameter  to  obtain  the  real  aperture. 

Size  of  Field.— The  field  of  the  telescope  is  determined  by 
noting  the  angle  between  the  extreme  rays  of  light  which 


62  THE  LEVEL. 

enter  the  effective  aperture  of  the  objective.  With  the  tran- 
sit telescope,  the  limiting  points  may  be  marked  on  the  side 
of  a  building  and  the  angle  measured  directly  with  the 
plates;  or  with  either  level  or  transit  the  angle  may  be  cal- 
culated from  the  measured  spread  in  a  given  distance.  For 
simplicity,  a  distance  of  57.3  feet  may  be  taken,  and  the  re- 
sult reduced  to  minutes. 

Magnifying  Power. — The  magnifying  power  of  a  tele- 
scope is  expressed  in  diameters,  or  as  the  multiplication  of 
linear  dimension.  It  is  determined  most  readily  by  IP  til?  ing 
an  observation  with  both  eyes  open,  one  looking  through 
the  telescope  and  the  other  by  natural  vision.  The  com- 
parison may  be  made  by  means  of  a  leveling  rod,  or  the 
courses  of  brick  or  weather-boarding  on  the  side  of  a  house 
may  be  used  in  like  manner. 

Parallax.— Parallax  is  the  apparent  movement  of  the 
cross-hairs  on  the  object  with  a  slight  movement  of  the  eye, 
and  is  due  to  imperfect  focusing  of  the  eyepiece  on  the 
cross-hairs  before  focusing  the  objective.  The  eyepiece 
should  be  focused  irith  tlie  eye  normal,  the  cross-hairs  being 
illuminated  by  holding  the  note  book  page  or  other  white 
object  a  few  inches  in  front  of  the  objective. 


Cross-Hairs. — The  cress-hairs  are  attached  to  a  ring  or 
reticule  which  is  held  by  two  pairs  of  capstan  headed  screws. 
The  hairs  usually  consist  of  spider  lines,  although  some 
makers  use  platinum  wires  for  the  purpose.  To  remove  the 
reticule  the  eyepiece  is  taken  out,  one  pair  of  screws  is  re- 
moved and  a  sharpened  stick  is  inserted  in  a  screw  hole.  The 
best  spider  lines  are  obtained  from  the  spider's  egg  nest. 

In  Fig.  17,  (a)  shows  the  usual  arrangement  of  the:  cross- 
hair ring- and  the  method  of  attaching  the  hairs;  (b)  shows 


THE  BUBBLE  VIAL.  63 

the  number  and  positions  of  hairs  used,  (1)  being  the  most 
common,  (2)  the  form  for  stadia  work  with  the  transit  and 
also  for  estimating  the  lengths  of  sights  with  the  level,  (3) 
a  form  used  by  some  makers  with  the  level,  and  (4)  a  style 
found  in  English  levels;  (c)  shows  the  egg  pod  or  case  of 
the  large  brown  spider  (about  half  size)  which  yields  the 
best  lines  for  engineering  instruments;  (d)  illustrates  a 
convenient  vest  pocket  outfit  for  replacing  cross-hairs  in 
the  field,  consisting  of  a  supply  of  spider  lines  and  some 
adhesive  paper  (bank  note  repair  paper)  each  in  a  capsule 
or  tin  tube,  and  several  sharpened  sticks  for  stretching  the 
hairs.  Cross-hairs  stretched  in  this  manner  may  last  indefi- 
nitely, or  they  may  be  fastened  on  permanently  with  shel- 
lac at  the  first  opportunity. 


THE  BUBBLE  VIAL. 

Principle.— The  spirit  level  consists  of  a  sealed  glass 
tube  nearly  filled  with  ether  or  other  liquid,  and  bent  or 
ground  so  that  the  action  of  gravity  on  the  liquid  may  indi- 
cate a  level  line  by  means  of  the  bubble.  The  delicacy  of  the 
bubble  depends  upon  the  radius  of  the  curvature  in  a  verti- 
cal plane,  the  greater  the  radius  the  more  delicate  the  level. 
Thus,  for  example,  a  perfectly  straight  tube  could  not  be 
used  as  a  level. 

Curvature  of  Bubble  Vials. — Good  bubble  vials  are  now 
made  by  grinding  or  polishing  the  interior  surface  of  a  se- 
lected glass  tube  by  revolution,  as  indicated  in  exaggerated 
form  at  (a)  Fig.  18.  As  a  general  rule,  only  one  side  of  the 
vial  is  actually  used,  it  being  customary  to  encase  it  in  a 
brass  tube  having  a  slot  or  race  on  one  side.  However, 
both  sides  of  the  vial  may  be  utilized,  as  in  (b)  and  (c).  Fig. 
18.  which  show  the  rcccrxioii  Icrel  adapted  to  the  transit  and 
wye  level,  respectively.  Bubble  vials  of  several  sizes  are 
shown  in  (d),  Fig.  18.  It  was  formerly  customary  to  grind 
out  only  a  portion  of  the  upper  side  of  the  glass  tube,  as 
shown  at  (e).  The  cheap  vial,  consisting  merely  of  a  bent 
tube,  used  mostly  in  carpenters'  and  masons'  levels,  is 
shown  at  (f);  and  a  method  of  increasing  the  precision  of 
the  bent  tube  by  lilting  it  is  indicated  at  (g)  Fig.  18.  . 


64 


THE  LEVEL. 


Fig.  18. 


Delicacy.— The  delicacy  of  the  bubble  vial  is  designated 
cither  by  the  radius,  usually  in  feet,  or  by  the  central  angle 
in  seconds  corresponding  to  one  division  or  one  inch  of  the 
bubble  scale.  Two  methods  are  employed  to  determine  the 
delicacy  of  level  vials,  (1)  by  the  optical  method,  as  at  (h), 
Fig.  18,  where  the  radius  is  calculated  from  an  observed  tar- 
get movement  at  a  given  distance  for  an  observed  bubble 
movement,  the  two  triangles  being  similar;  and  (2)  by  the 
level  tester,  as  at  (i),  by  means  of  which  the  angular  move- 
ment is  read  from  the  micrometer  head  for  a  given  move- 
ment of  the  bubble.  The  engineer  usually  employs  the  radial 
designation,  while  the  maker  expresses  the  delicacy  in  an- 
gular units.  As  shown  at  (h)  and  (i),  Fig.  18,  the  radius  in 
feet  is  equal  to  17,189  divided  by  seconds  per  inch  of  bubble. 

Bubble  Line.— The  relations  of  the  bubble  to  the  other 
parts  of  the  instrument  are  best  understood  by  representing 


LEVELING  RODS. 


65 


the  vial  by  a  line.  This  line  may  be  either  the  axis  of  the 
surface  of  revolution  in  (a),  Pig.  18,  or  to  provide  for  either 
of  the  three  forms  of  vial  shown,  it  may  be  taken  as  the 
tangent  line  at  the  middle  or  top  point.  This  tangent  line 
will  be  meant  hereafter  in  referring  to  the  bubble  line. 


(dt 


Fig.  19. 


th) 


(I) 


rg) 


LEVELING  RODS. 

Types.— There  are  two  classes  or  types  of  leveling  rods; 
(1)  target  rods,  having  a  sliding  target  which  Is  brought 
into  the  line  of  sight  by  signals  from  the  leveler;  and  (2) 
self -read  ing  or  speaking  rods  which  are  read  directly  by  the 
leveler. 


66  THE  LEVEL. 

In  Fig.  19,  (a)  is  the  Philadelphia  rod;  (b)  the  New  York 
rod;  and  (c)  the  Boston  rod.  The  first  is  either  a  target 
or  self-reading  rod;  the  second  is  a  target  rod,  but  may  be 
read  from  the  instrument  when  the  rod  is  "short";  the  Bos- 
ton rod  is  strictly  a  target  rod.  The  Philadelphia  rod  is 
perhaps  the  favorite  for  most  purposes,  and  the  Boston  rod 
is  used  least.  A  folding  self-reading  rod  is  shown  at  (d), 
Fig.  19;  (e)  is  a  woven  pocket  device  which  may  be  tacked 
to  a  strip  of  wood  and  used  as  a  leveling  rod;  (f)  is  a  rail- 
road contouring  rod  with  an  adjustable  base;  (g)  is  a  plain 
rod  graduated  to  feet,  for  use  with  the  water  level. 

Targets. — The  targets  shown  on  the  Philadelphia  and 
New  York  rods,  (a)  and  (b),  Fig.  19,  are  called  quadrant 
targets.  That  on  the  Boston  rod,  (c),  is  a  modified  form  of 
the  diamond  target.  A  special  form,  called  the  corner  tar- 
get, is  turned  on  two  sides  of  the  rod  to  assist  in  plumb- 
ing the  rod,  and  another  target  has  two  parallel  planes  for 
the  same  purpose.  A  detachable  rod  level  is  shown  at  (h). 
The  target  on  rod  (b),  with  the  zero  of  the  vernier  0.09  foot 
below  the  center  of  the  target,  frequently  causes  blunders. 

USE  OF  THE  LEVEL. 

Use. — The  engineers'  level  is  used:  (1)  to  determine  dif- 
ferences of  elevation;  (2)  to  make  profile  surveys;  (3)  to 
locate  contours;  (4)  to  establish  grade  lines;  (5)  to  cross- 
section;  (6)  to  run  lines. 

Differential  Leveling. — Differential  leveling  consists 
of  finding  the  difference  of  elevation  between  two  or  more 
points.  In  the  simplest  case  the  difference  of  elevation  be- 
tween two  points  may  be  found  from  a  single  setting  of 
the  level,  the  leveling  rod  being  used  to  determine  the 
vertical  distance  from  the  plane  of  the  instrument  to  each 
of  the  two  points,  and  the  difference  between  the  rod  read- 
ings taken.  When  the  distance  between  the  two  points  is 
too  great,  either  vertically  or  horizontally,  or  both,  to  ad- 
mit of  this  simple  process,  two  or  more  settings  of  the  level 
are  taken  so  as  to  secure  a  connected  series  of  rod  read- 
ings, the  algebraic  sum  of  which  gives  the  desired  differ- 
ence of  elevation.  This  difference  may  be  expressed  either 
by  the  numerical  result  of  the  algebraic  sum  of  the  rod 
readings,  or  by  assuming  an  elevation  for  the  beginning 


USE  OF  THE  LEVEL.  67 

point  and  calculating  the  elevation  of  the  closing  point  by 
means  of  the  observed  rod  readings. 

A  back  sight  is  a  rod  reading  taken  to  determine  the  height 
of  the  instrument.  A  fore  sight  is  a  rod  reading  taken  to  de- 
termine the  height  of  a  point.  A  bench  mark  is  a  point  se- 
lected or  established  for  permanent  reference  in  leveling 
operations.  A  turning  point  is  a  temporary  reference  point 
used  in  moving  the  instrument  ahead  to  a  new  setting.  The 
same  point  is  often  both  a  turning  point  and  bench  mark. 
The  datum  is  the  plane  or  surface  of  reference  from  which 
the  elevations  are  reckoned;  it  may  be  sea  level,  or  an  arbi- 
trary local  datum.  A  level  line  is  a  line  parallel  to  the  sur- 
face of  a  smooth  body  of  water.  A  horizontal  line  is  tangent 
to  a  level  line  at  any  point.  The  curvature  varies  as  the 
square  of  the  distance  from  the  point  of  tangeiicy,  and  is 
0.001  foot  in  204  feet,  or  8  inches  in  one  mile. 

In  Fig.  19,  (i)  shows  a  metal  and  also  a  wooden  peg  com- 
monly used  for  turning  points.  Several  forms  of  bench 
marks  are  shown  in  Fig.  19;  (j)  is  a  mark  on  the  corner 
of  a  stone  water-table;  (k)  a  rivet  leaded  into  a  hole 
drilled  in  a  stone  slab,  (1)  a  railroad  spike  driven  into  a 
wooden  post  or  telegraph  pole;  (m)  a  projection  cut  on  the 
root  of  a  tree,  preferably  with  a  spike  driven  vertically  into- 
the  top  of  the  bench,  and  usually  with  a  blaze  alsove 
marked  "B.  M.  No.—."  All  bench  marks  and  also  turning 
points  should  be  clearly  described  in  the  notes. 

Two  chief  essentials  in  correct  differential  leveling  are. 
(1)  that  the  bubble  be  in  exactly  the  same  position  (usu- 
ally the  middle)  on  both  back  and  fore  sight;  and  (2)  that 
the  length  of  back  sight  and  fore  sight,  horizontally,  shall 
be  balanced.  It  is  seen  at  (e),  Fig.  16,  that  with  the  bubble 
always  in  the  middle,  the  line  of  collimation  generates  a 
horizontal  plane  when  in  perfect  adjustment,  but  a  cone  with 
axis  vertical  when  out  of  adjustment;  so  that  ir.  taking 
equal  distances  in  the  opposite  directions,  the  base  of  the 
con"  is  used,  this  base  being  parallel  to  the  true  collima- 
tion plane.  In  the  best  leveling  practice  the  instru- 
ment is  adjusted  as  perfectly  as  possible  and  then  used  so  that 
the  residual  errors  balance  each  other. 

The  three  common  styles  of  leveling  rod  may  be  read  to 
0.001  foot  by  vernier  or  by  estimation  on  a  scale  of  0.005 
foot.  However,  for  most  kinds  of  leveling,  it  is  an  absurd 


68  THE  LEVEL. 

refinement  to  read  the  rod  closer  than  0.01  foot,  especially 
with  the  usual  maximum  length  of  sight  of  350  to  400  feet, 
and  with  the  more  or  less  sluggish  bubbles  supplied  in  the 
general  run  of  leveling  instruments.  Furthermore,  the 
horizontal  hair  usually  covers  0.01  foot  or  so  of  the  target 
at  the  maximum  length  of  sight,  that  is,  the  target  can  move 
that  amount  without  being  noticed  by  the  observer. 

Profile  Leveling.— Profile  leveling  consists  of  finding 
the  relative  elevations  of  a  series  of  representative  points 
along  a  surveyed  line,  for  the  purpose  of  constructing  a  pro- 
file or  vertical  section.  The  skeleton  of  profile  leveling,  that 
is,  the  precise  bench  marks  and  turning  points  with  the 
successive  heights  of  instrument,  is  identical  with  differen- 
tial leveling,  already  described.  Having  determined  the 
height  of  instrument  by  taking  a  back  sight  on  a  bench 
mark  of  known  or  assumed  elevation,  rod  readings  are 
taken  at  proper  intervals  along  the  measured  and  staked 
line.  These  readings  are  fore  sights,  but  they  are  usually 
termed  intermediate  sights  to  distinguish  them  from  the 
more  precise  rod  readings  taken  on  turning  points  and 
bench  marks.  On  railroad  surveys  intermediate  sights  are 
taken  usually  to  the  nearest  0.1  foot  on  the  ground;  but  in 
other  cases,  such  as  tile  and  sewer  surveys,  intermediates 
are  often  read  to  the  nearest  0.01  foot  on  small  pegs  driven 
beside  the  station  stakes  flus'h  with  the  surface  of  the 
ground.  In  railroad  work,  the  benches,  turning  points, 
and  intermediates  of  special  importance  are  commonly  read 
to  0.01  foot,  although  some  engineers  persist  in  the  ques- 
tionable practice  of  taking  the  nearest  0.001.  In  drainage 
surveys  the  nearest  0.01  foot  is  usually  taken  on  bench 
marks,  although  more  carefully  than  on  the  intermediate 
peg  points,  and  the  nearest  0.1  foot  is  read  on  ground  points. 

The  errors  of  profile  leveling  are  balanced  on  turning 
points  by  equal  back  and  fore  sights,  as  in  differential  lev- 
eling. If  the  instrument  is  seriously  out  of  adjustment,  an 
error  is  made  in  the  case  of  odd  bench  marks  with  unbal- 
anced sights,  and  also  on  all  intermediate  sights.  However, 
the  error  is  usually  unimportant  when  ground  readings  are 
taken  to  the  nearest  0.1  foot.  In  important  leveling,  such 
as  canal  and  drainage  work,  it  is  customary  to  run  a  line  of 
check  levels  to  prove  the  benches,  before  construction  be- 
gins. 


USE  OF' THE  LEVEL.  6d 

The  profile  is  plotted  to  an  exaggerated  scale  vertically 
on  a  special  paper,  called  profile  paper.  Three  kinds,  known 
as  plates  A,  B  and  C,  are  in  general  use.  The  most  common 
is  plate  A,  which  is  ruled  in  i/i-inch  squares  with  a  further 
subdivision  to  1-20  inch  vertically.  In  railroad  profiles  the 
scales  most  used  are  400  feet  to  the  inch  horizontally  and 
20  feet  vertically.  A  still  greater  exaggeration  is  generally 
used  in  drainage  profiles. 

Contour  Leveling.— Contour  leveling  is  an  application 
of  the  methods  of  profile  leveling  to  the  location  of  contour 
lines,  that  is,  lines  having  the  same  elevation.  Two  methods 
are  employed:  either  (1)  actually  establishing  points  on 
the  adopted  contour  planes  on  the  ground  and  then  locat- 
ing these  points;  or  (2)  taking  random  elevations  at  rep- 
resentative points  and  interpolating  the  contour  lines  from 
the  plotted  data.  The  latter  is  the  more  common.  The 
chief  purpose  of  contour  leveling  is  to  make  a  contour  map, 
and  the  process  is  essentially  a  part  of  topographic  survey- 
ing, where  it  will  be  more  fully  considered. 

Grade  Lines. — The  establishment  of  grade  lines  is  usti- 
ally  the  concluding  part  of  profile  leveling.  After  making 
the  profile,  the  grade  line  is  established  by  stretching  a  fine 
thread  through  the  ruling  points,  taking  into  account  the 
controlling  conditions,  such  as  maximum  gradient  or  earth- 
work quantities  on  a  railroad  profile,  the  carrying  capacity 
or  the  scour  in  the  case  of  a  ditch,  etc.  After  laying  the 
grade  line  on  the  profile,  notes  are  made  of  the  data,  and 
the  actual  grade  line  is  established.  Two  methods  are  used: 
(1)  the  height  of  instrument  is  determined  as  usual,  and 
stakes  are  driven  at  measured  intervals  with  their  tops  to 
match  calculated  rod  readings;  and  (2)  a  limited  number 
of  ruling  points  are  established  by  the  first  method  or 
otherwise,  and  the  remaining  stakes  are  "shot  in"  by  con- 
structing a  line  parallel  to  the  ruling  line  used.  The  latter 
is  more  rapid,  since  a  constant  rod  reading  is  used;  how- 
ever, the  method  is  unreliable  unless  the  fore  sight  be 
checked  frequently  on  a  fixed  target. 

Cross-Sectioning.— Cross-sectioning  consists  of  staking 
out  the  limits  of  the  transverse  section  of  an  excavation  or 
embankment  for  the  purpose  of  construction,  and  usually 
includes  the  collection  of  data  for  the  calculation  of  the 
quantities.  This  may  be  done  either  with  the  engineers' 


70  THE  LEVEL. 

level,  rod  and  tape  line,  or  with  special  rods  called  cross- 
section  rods.  The  notes  are  taken  as  rectangular  coordi- 
nates, usually  with  reference  to  the  center  of  the  finished 
roadbed.  The  slope  stakes  are  set  where  the  side  slope  lines 
pierce  the  surface  of  the  ground. 

Running  Lines. — Lines  are  sometimes  run  with  the  en- 
gineers' level,  provision  being  made  in  most  good  levels  for 
the  attachment  of  a  plumb  bob.  A  line  may  be  prolonged 
by  sighting  in  two  points  ahead.  A  clamp  and  tangent 
movement  are  necessary.  Some  builders'  levels  have  a 
needle  and  also  a  roughly  divided  horizontal  circle  for  use 
in  staking  out  buildings. 

Practical  Hints.— The  following  practical  suggestions 
apply  more  or  less  directly  to  all  kinds  of  leveling,  and  also 
in  a  general  sense  to  transit  work. 

Speed.— Cultivate  the  habit  of  briskness  in  all  the  de- 
tails of  the  work.  While  undue  haste  lowers  the  standard 
of  the  results,  an  effort  should  be  made  to  gain  speed 
steadily  without  sacrificing  precision.  Gain  time  for  the 
more  important  details  by  moving  rapidly  from  point  to 
point.  On  rapid  surveys  both  leveler  and  rodman  often  move 
in  a  trot.  Neither  rodman  nor  leveler  should  delay  the 
other  needlessly. 

Care  of  Instruments. — Do  not  carry  the  level  on  the  shoul- 
der in  climbing  fences.  Clamp  the  telescope  slightly  when 
hanging  down.  Keep  the  tripod  legs  at  the  proper  tight- 
ness, and  avoid  looseness  in  the  tripod  shoes.  Avoid  undue 
exposure  to  the  elements,  and  guard  the  level  from  injury. 
Do  not  leave  the  instrument  standing  on  the  tripod  in  a 
room  over  night. 

Setting  Up. — In  choosing  a  place  to  set  the  level  up,  con- 
sider visibility  and  elevation  of  back  point  and  probable 
fore  sight.  Set  up  with  plates  about  level.  On  side-hill 
ground  place  one  leg  up  hill.  In  general,  place  two  tripod 
shoes  parallel  to  the  general  line  of  the  levels. 

Leveling  Up.— A  pair  of  foot  screws  should  be  shifted  to 
the  general  direction  of  the  back  or  fore  sight  before  level- 
ing up.  Set  the  foot  screws  up  just  to  a  snug  bearing  and 
no  tighter.  If  either  pair  of  screws  binds,  loosen  the  other 
pair  a  little.  The  bubble  moves  with  the  left  thumb.  Level 
up  more  precisely  in  the  direction  of  the  sight  than  trans- 
verse to  it,  but  do  not  neglect  the  latter.  Inspect  the  bubble 


USE  OF  THE  LEVEL.  71 

squarely  to  avoid  parallax,  and  also  to  prevent  such  blun- 
ders as  reading  the  bubble  five  spaces  off  center. 

OUscrcationn.— Adjust  the  eyepiece  for  parallax  with  the 
eye  unstrained.  It  is  much  easier  on  the  eyes  to  observe 
with  both  eyes  open.  Read  at  the  intersection  of  the  cross- 
hairs, since  the  horizontal  hair  may  be  inclined.  Set  the 
target  approximately,  check  the  bubble,  and  repeat  the  pro- 
cess several  times  before  approving  the  sight.  Be  certain 
that  the  bubble  is  exactly  in  the  middle  at  the  instant  of 
approving  the  target.  If  the  level  has  horizontal  stadia 
lines,  beware  of  reading  the  wrong  hair  (the  reticule  may  be 
rotated  one-quarter  so  as  to  have  the  extra  hairs  vertical, 
or  a  filament  may  be  attached  to  the  middle  horizontal  hair 
to  assist  in  identifying  it).  Avoid  disturbance  of  the  tripod 
by  stepping  about  the  instrument.  Assist  the  rodman  in 
plumbing  the  rod.  Let  signals  be  perfectly  definite  both  as 
to  direction  and  amount,  using  the  left  hand  for  "up"  and 
the  right  for  "down",  or  vice  versa. 

The  leveler  can  work  much  more  intelligently  if  he  knows 
the  space  covered  on  the  rod  by  one  division  of  the  bubble 
scale  at  the  maximum  length  of  sight,  and  also  the  space 
on  the  rod  hidden  by  the  cross-hair. 

Balancing  Sights.— Balance  the  length  of  back  sight  and 
fore  sight,  and  record  the  approximate  distances.  The  dis- 
tances in  the  two  directions  may  be  made  equal  roughly  by 
equality  of  focus,  but  it  is  better  on  careful  work  to  pace 
the  distances  or  determine  them  by  means  of  the  stadia 
lines  in  the  level.  If  necessary  to  unbalance  the  sights, 
they  should  be  balanced  up  at  the  first  opportunity,  and  in 
general  they  should  be  in  balance  when  closing  on  import- 
ant benches.  When  leveling  up  or  down  steep  slopes,  fol- 
low a  zigzag  course  to  avoid  short  sights.  Take  no  sights 
longer  than  350  or  400  feet. 

Leveling  Rod. — The  rod  should  be  carefully  plumbed,  to 
accomplish  which  the  rodman  should  stand  squarely  behind 
the  rod  and  support  it  symmetrically  between  the  tips  of 
the  extended  fingers  of  the  two  hands.  With  "short"  rods 
avoid  the  somewhat  common  blunder  of  0.09  foot  when  the 
vernier  slot  is  below  the  center  of  the  target.  With  "long" 
rods,  see  that  the  target  has  not  slipped  from  its  true  set- 
ting before  reading  the  rod.  Read  the  rod  at  least  twice, 
and  avoid  blunders  of  1  foot,  0.1  foot,  etc.  Careless  rodmen 


72  THE  LEVEL. 

sometimes  invert  the  rod.  Each  rod  reading  on  turning 
points  and  bench  marks  should,  when  practicable,  be  read 
independently  by  both  rodman  and  leveler. 

Bench  Marks  and  Turnlinj  Points. — Wooden  pegs  or  other 
substantial  points  should  be  used  to  turn  the  instrument 
on.  Select  bench  marks  with  reference  to  ease  of  identifica- 
tion, the  balancing  of  sights,  freedom  from  disturbance,  etc. 
As  a  rule,  each  bench  mark  should  be  used  as  a  turning 
point  so  that  the  final  closure  of  the  circuit  may  prove  the 
bench. 

Record  and  Calculations.— Describe  bench  marks  and  turn- 
ing points  clearly.  It  is  good  practice  to  apply  algebraic 
signs  to  the  back  and  fore  sight  rod  readings.  The  eleva- 
tions should  be  calculated  as  fast  as  the  rod  readings  are 
taken,  and  calculations  on  turning  points  should  be  made 
independently  by  leveler  and  rodman,  and  results  compared 
at  each  point.  The  rodman  may  keef)  turning  point  notes 
in  the  form  of  a  single  column.  The  calculations  should  be 
further  verified  by  adding  up  the  columns  of  back  sights 
and  fore  sights  for  each  circuit,  or  page,  or  day's  work,  and 
the  algebraic  sum  of  the  two  compared  with  the  difference 
between  the  initial  and  last  calculated  elevation. 

Error  of  Closure. — A  circuit  of  levels  run  with  a  good 
level  by  careful  men,  observing  all  the  foregoing  pre- 
cautions, should  check  within  0.05  foot  into  the  square  root 
of  the  length  of  the  circuit  in  miles  (equivalent  to  0.007  foot 
into  the  square  root  of  the  length  of  the  circuit  in  100-foot 
stations.)  In  closing  a  circuit,  the  error  should  be  care- 
fully determined,  as  above  indicated,  and  the  value  of  the 
coefficient  of  precision  found.  (See  discussion  of  errors  of 
leveling  and  precision  diagrams  in  the  chapter  on  errors  of 
surveying.) 

ADJUSTMENT  OF  THE  WYE  LEVEL. 

Elementary  Lines.— The  principal  elementary  lines  of 
the  wye  level,  as  shown  in  Fig.  16,  are:  (1)  the  line  of  col- 
limation;  (2)  the  bubble  line;  (3)  the  vertical  axis.  For 
the  purpose  of  adjustment  there  should  be  added  to  these: 
(4)  the  axis  of  the  rings;  (5)  the  bottom  element  of  the 
rings.  The  following  relations  should  exist  between  these 
lines;  (a)  the  line  of  collimation  and  bubble  line  should  be 


ADJUSTMENT  OF  THE  LEVEL.  73 

parallel;  (b)  the  bubble  line  should  be  perpendicular  to  the 
vertical  axis.  The  first  of  these  relations  involves  two 
steps,  viz.,  (1)  to  make  the  bubble  line  parallel  to  the  bot- 
tom element  of  the  rings,  and  (2)  to  make  the  line  of  col- 
limation coincide  with  the  axis  of  the  rings.  The  other 
relation  involves  the  wye  adjustment,  and  is  similar  to  the 
plate  level  adjustment  described  in  the  chapter  on  the  com- 
pass. 

Bubble. — To  make  the  bubble  line  parallel  to  the  bottom 
element  of  the  rinyx. — Two  steps  are  involved,  (a)  to  place 
the  bubble  line  I'M  the  same  plane  with  the  bottom  element, 
and  (b)  to  make  the  two  lines  parallel. 

Azimuth  Xereirx. — To  make  the  bubble  line  in  the  same  plane 
iritJt  tlie  bottom  element  of  the  rinyx. — Clamp  the  level  over  a 
pair  of  foot  screws,  loosen  the  wye  clips,  and  level  up;  ro- 
tate the  telescope  through  a  small  angle,  and  if  the  bubble 
moves  away  from  the  middle,  bring  it  back  by  means  of  the 
azimuth  adjusting  screws.  Test  by  rotating  in  the  opposite 
direction.  Leave  the  screws  snug. 

Altitude  Screirs — To  make  the  bubble  line  and  tlie  bottom  ele- 
ment of  the  rinyx  parallel  —Make  the  element  level 
with  the  foot  screws  and  bring  the  bubble  to  the  middle  by 
means  of  the  <iltitud<  adjusting  screws.  The  element  is 
made  level  by  the  method  of  reversions  as  follows:  With 
the  level  clamped  over  a  pair  of  foot  screws,  as  above,  lift 
the  clips  and  level  up  precisely;  cautiously  lift  the  tele- 
scope out  of  the  wyes,  turn  it  end  for  end,  and  rrry  yentlii 
replace  it  in  the  wyes;  if  the  bubble  moves,  bring  it  half 
way  back  by  means  of  the  foot  screirx.  Before  disturbing 
adjusting  screws  make  several  reversals,  and  conclude  the 
adjustment  with  screws  snug.  This  end  for  end  reversal 
is  similar  to  that  made  with  the  carpenter's  level,  the 
straight  edge  of  the  level  corresponding  to  the  element  of 
the  rings.  The  lines  involved  are  shown  in  Fig.  16. 

Line  of  Collimation — To  make  the  line  of  coll imat Ion 
rninr-ide  icith  the  a.cis  of  the  rinys. — Loosen  clips,  sight  on  a 
point,  say  a  nail  head  or  the  level  target,  more  distant  than 
the  longest  sight  used  in  leveling;  rotate  the  telescope  half 
way  and  note  the  movement  of  the  hair,  if  any.  The  line 
of  collimation  generates  a  cone,  the  axis  of  which  is  that 
of  the  rings,  and  the  apex  of  which  is  at  the  optical  center 
of  the  objective.  Correct  one-half  the  observed  error  by 


74  THE  LEVEL. 

means  of  the  capstan  headed  screws  which  hold  the  cross- 
hair ring.  Gradually  perfect  the  adjustment  until  the  in- 
tersection of  the  oross-hairs  remains  fixed  on  the  same 
point  when  reversed  by  rotation  with  reference  to  either 
hair.  The  adjustment  should  be  concluded  with  the  screws 
at  a  snug  bearing. 

After  collimating  the  instrument  for  a  long  distance,  the 
adjustment  should  be  checked  for  a  short  distance,  say  50 
or  100  feet,  so  as  to  test  the  motion  of  the  optical  center 
of  the  objective. 

Rings. — The  theory  of  tlif  wye  lerel  demands  perfect  equality 
of  the  rings,  that  is,  the  parallelism  of  the  axis  and  element, 
as  in  (c),  Fig.  16.  Should  the  rings  be  unequal,  either  from 
poor  workmanship  or  uneven  wear  in  service,  they  form  a 
cone  instead  of  a  cylinder,  and  the  axis  is  not  parallel  to  the 
element,  as  in  (d),  Fig.  16.  Under  the  latter  conditions,  the 
principle  of  the  wye  level  fails,  and  an  independent  test  is 
demanded.  This  is  known  as  the  two-peg  test,  the  de- 
tails of  which  are  shown  in  (e)  and  (f),  Fig.  16,  and  de- 
scribed in  the  adjustments  of  the  dumpy  level.  If,  after 
making  the  wye  level  adjustments  above  described,  the  two- 
peg  test  shows  that  the  line  of  collimation  and  bubble  line 
are  not  parallel,  the  rings  are  probably  unequal  and  the  in- 
strument should  thereafter  be  adjusted  as  a  dumpy  level. 
However,  hasty  conclusions  should  be  guarded  against. 

In  case  the  instrument  has  a  reversion  level,  shown 
at  (c),  Fig.  18,  the  equality  of  the  rings  may  be  tested  by 
first  adjusting  the  top  tangent  line  of  the  bubble  vial  par- 
allel to  the  bottom  element  of  the  rings,  and  then  after  ro- 
tating the  telescope  half  way  round  in  the  wyes,  compare 
the  bottom  (now  above)  tangent  line  of  the  vial  with  the 
top  (now  below)  element  of  the  rings,  all  by  the  end  for 
end  reversion.  However,  the  exact  parallelism  of  the  top 
and  bottom  tangent  lines  of  the  reversion  level  should  first 
be  proven  by  the  two-peg  method. 

Wyes. — To  make  bubble  line  perpendicular  to  the  rertical 
a.ris. — Make  the  vertical  axis  vertical  and  bring  the  bubble  to 
the  middle  by  means  of  the  tri/e  mitx.  The  vertical  axis  is 
made  vertical  by  reversion  thus:  With  clips  pinned,  level 
up;  reverse  over  the  same  pair  of  screws,  and  bring  the 
bubble  half  way  back  with  the  foot  screws.  When  adjusted, 
the  bubble  will  remain  in  the  middle  during  a  complete  rev- 


ADJUSTMENT  OF  THE  LEVEL.  75 

olution.  This  adjustment  is  identical  in  principle  with  the 
plate  level  adjustment  of  the  compass  and  transit,  illus- 
trated in  (a),  Fig.  13.  The  wye  adjustment  should  follow 
the  adjustment  of  the  bubble  line  parallel  to  the  element 
of  the  rings.  The  wye  adjustment  is  a  convenience,  not 
a  necessity. 

Centering  the  Eyepiece. — After  collimating  the  level, 
the  cross-hairs  should  appear  in  the  center  of  the  field.  The 
eyepiece  is  centered  by  moving  its  ring  held  by  four  screws. 
This  adjustment  is  desirable,  but  not  essential. 

ADJUSTMENT  OF  THE  DUMPY  LEVEL. 

Elementary  Lines.— The  principal  elementary  lines  of 
the  dumpy  level  are  identical  with  those  of  the  wye  level: 
(1)  the  line  of  collimation;  (2)  the  bubble  line;  (3)  the  ver- 
tical axis.  As  in  the  wye  level,  the  bubble  line  should  be 
(1)  perpendicular  to  the  vertical  axis,  and  (2)  parallel  to 
the  line  of  collimation.  However,  owing  to  the  difference 
in  the  construction  of  the  two  types  of  instrument,  the 
auxiliary  elementary  lines  are  not  recognized  in  the  dumpy 
level.  The  transit  with  its  attached  level  is  identical  in 
principle  with  the  dumpy  level. 

Bubble. — To  make  the  bubble  line  perpendicular  to  the  ver- 
tical axix. — Make  the  vertical  axis  vertical  by  the  method  of 
reversions,  and  adjust  the  bubble  to  the  middle.  This  adjust- 
ment is  identical  in  principle  with  the  plate  level  adjust- 
ment, shown  in  (a),  Fig.  13.  The  bubble  should  remain  in 
the  middle  through  a  complete  revolution. 

Line  of  Collimation. — To  make  the  line  of  collimation 
parallel  to  the  bubble  line. — Construct  a  level  line,  and  adjust 
the  cross-hairs  to  agree  with,  it.  The  level  line  is  determined 
either  by  using  the  surface  of  a  pond  of  water,  or  by  driv- 
ing two  pegs  at  equal  distances  in  opposite  directions  from 
the  instrument,  and  taking  careful  rod  readings  on  them 
with  the  bubble  precisely  in  the  middle,  as  shown  at  (e), 
Fig.  16.  For  simplicity,  the  two  pegs  may  be  driven  to  the 
same  level,  or  two  spikes  may  be  driven  at  the  same  level 
in  the  sides  of  two  fence  posts,  say  400  feet  apart.  Other- 
wise, determine  the  precise  difference  of  elevation,  as  indi- 
cated in  (e),  Fig.  16.  Then  set  the  level  almost  over  one  of 
the  pegs,  level  up,  and  as  in  the  first  method  of  (f),  Fig.  16, 


76  THE  LEVEL. 

set  the  target  of  the  leveling  rod  at  the  line  of  coliimation, 
as  indicated  by  the  center  of  the  object  glass  cr  eyepiece, 
(this  can  be  done  more  precisely  than  most  levels  will  set 
the  target  at  400  feet  distance);  now  with  the  rod  on  the 
other  peg,  sight  at  the  target  (shifted  to  allow  for  the  dif- 
ference if  the  two  pegs  are  not  on  the  same  level);  adjust 
the  cross-hair  to  the  level  line  so  constructed.  If  preferred, 
the  second  method  shown  in  (f),  Pig.  16,  may  be  used;  the 
level  is  set  back  of  one  peg,  rod  readings  are  taken  on  both 
pegs,  allowance  made  for  the  difference  in  level  of  the  two 
pegs,  if  any,  the  inclination  of  the,  line  of  coliimation  deter- 
mined, correction  made  for  the  small  triangle  from  the 
level  to  the  first  peg,  and  finally  the  level  line  constructed 
by  means  of  the  calculated  rod  readings.  The  second 
method  is  simplified  and  made  practically  equivalent  to  the 
first  by  setting  the  level  at  minimum  focusing  distance  from 
the  first  peg.  The  small  corrective  triangle  is  thus  practi- 
cally eliminated.  This  process  is  called  the  two-peg  ad- 
justment. 

The  foregoing  method  ignores  curvature  of  the  earth 
(equal  to  0.001  foot  in  about  2CO  feet,  or  0.004  foot  in  400 
feet)  which  is  less  than  the  error  of  observation  with  most 
levels. 

Uprights.--In  some  dumpy  levels  the  uprights  which 
connect  the  telescope  with  the  level  bar  are  adjustable, 
similar  to  the  wyes  of  the  wye  level.  This  adjustment  is 
designed  to  bring  the  bubble  line  perpendicular  to  the  ver- 
tical axis  in  case  the  bubble  is  first  adjusted  parallel  to  the 
line  of  coliimation.  However,  the  best  order  is  that  already 
described,  viz.,  first  adjust  the  bubble  line  perpendicular 
to  the  vertical  axis,  and  then  the  line  of  coliimation  par- 
allel to  the  bubble  line,  in  which  case  the  adjustable  up- 
rights are  unnecessary. 

PROBLEMS  WITH  THE  LEVEL. 

PROBLEM  Cl.  DIFFERENTIAL  LEVELING  WITH  THE 
HAND  LEVEL  (OR  WATER  LEVEL.) 

(a)  Equipment. — Hand  level  (or  water  level),  rod  gradu- 
ated to  feet. 

(b)  Problem. — Run  an  assigned  level  circuit  with  the  hand 


PROBLEMS. 


77 


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78  THE   LEVEL. 

level  (or  water  level),  observing  the  nearest  0.1  foot  by  es- 
timation, and  closing  back  on  the  starting  point. 

(c)  Methods. — (1)  Determine  the  correct  position  of  the 
bubble  of  the  hand  level  by  sighting  along  a  water  table, 
or  sill  course  of  a  building,  or  by  the  principles  of  the  two- 
peg  test.  (If  the  water  level  is  used,  fill  the  tube  so  as  to 
have  a  good  exposure  of  the  colored  water  in  the  glass  up- 
rights.) (2)  Take  sights  of  100  feet  or  so  (paced),  estimat- 
ing the  rod  reading  to  the  nearest  0.1  foot;  balance  back 
and  fore  sights;  assume  the  elevation  of  the  starting  point, 
and  keep  the  notes  in  a  single  column  by  addition  and  sub- 
traction. (3)  Check  back  on  the  first  point.  Determine  the 
coefficient  of  precision. 

PROBLEM  C2.  DIFFERENTIAL  LEVELING  WITH  EN- 
GINEERS' LEVEL  (OR  TRANSIT  WITH  ATTACHED 
LEVEL). 

I 

(a)  Equipment. — Engineers'  level  (or  transit  with  attached 
level),  leveling  rod,  hatchet,  pegs,  spikes. 

(b)  Problem. — Run  the  assigned  level  circuit,   observing 
the  nearest  0.01  foot,  and  closing  back  on  the  initial  point. 

(c)  Methods. — Follow  the  practical  suggestions  given  at 
the  conclusion  of  the  "Use  of  the  Level,"  giving  special  at- 
tention to  the  following  points:      (1)  eliminate  parallax  of 
tthe  eyepiece;  (2)  balance  back  and  fore  sight  distances;  (3) 
have  the  bubble  precisely  in  the  middle  at  the  instant  of 
sighting;    (4)   both  rodman  and  leveler  read  each  rod  and 
also  make  the  calculations  independently;  (5)  calculate  ele-- 
vations  as  rapidly  as  rod  readings  are  obtained;   (6)  plumb 
the  rod;    (7)   avoid  blunders;    (8)   determine  coefficient   of 
precision;    (9)  no  sights  longer  than  350  or  400  feet.     Fol- 
low the  first  form  shown   to   begin   with, — the   other   after 
several  circuits  have  been  run. 

PROBLEM  C3.  PROFILE  LEVELING  FOR  A  DRAIN. 

(a)  Equipment. — Engineers'  leveling  instrument,  leveling 
rod,  100-foot  steel  tape,  stakes,  pegs,  axe. 

(b)  Problem.— Make  a  survey,  plat  and  profile,  with  esti- 
mate of  cuts  and  quantities  for  a  drain  under  assigned  con- 
ditions. 


PROBLEMS. 


79 


SURVEY     FOB     A    DRAIN     FROM 

D..crlpti.n. 


fffom  pipm  ///T*    A>  Cert-itrvotor-y. 

*ai/*    of  main  trvtK,    t/.l  C.St.Ay. 
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point  3'W.o>not  2'J.    o/"  /V.*K  Cot-, 
of  £no.  Lab.    Lin*    runs     tA+nce 

Of    Spr;n9fi*l<*  Av*.     J/»/r«     <,r* 
S9t    2'   f»  *9.   <*f  ^reposed   frrnc,* 

ftojh  *v//A  ^ot/nrf  £«/<*>  sfa/fes. 


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NOT 

6     FO 

t    A    C 

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M     ENGINEERING     LABORATORY. 

too.oo 

J.enol  Jtont  tiff,  Hr.ofoor,  fny.  Lat,. 

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THE  LEVEL. 


(c)  Methods. — (1)  Examine  the  ground,  determine  the 
head  and  outlet  of  the  drain,  and  select  the  general  route. 
(2)  Stake  out  the  line,  set  stakes  every  50  feet,  or  oftener 
if  required  to  get  a  good  profile,  and  drive  a  ground  peg 
flush,  say  2  feet  to  the  right  (or  left)  of  each  stake;  record 
data  for  mapping  the  line.  (3)  Starting  with  the  assigned 
datum  or  bench  mark,  run  levels  over  the  line  of  the  pro- 
posed drain,  observing  the  nearest  0.01  foot  both  on  turning 
points  and  ground  pegs,  the  former  somewhat  more  care- 
fully; take  rough  ground  levels,  as  required,  to  the  nearest 
0.1  foot;  locate  and  determine  the  depth  of  intersecting 
drains  or  pipe  lines,  or  other  objects  which  may  influence 
the  grade  line  of  the  drain,  and  secure  full  data  for  placing 
the  same  on  the  profile;  observe  due  care  with  the  back  and 
fore  sights,  as  in  differential  leveling,  and  conclude  the 
leveling  work  with  a  line  of  check  levels  back  to  the  initial 
bench  mark;  a  permanent  bench  mark  should  be  established 
at  each  end  of  the  drain,  and  if  the  length  is  considerable, 
at  one  or  more  intermediate  points  as  well.  (4)  Make  plat 
and  profile  of  the  drain  line;  lay  the  grade  line,  taking  into 
account  all  ruling  points;  calculate  the  cuts,  both  to  the 
nearest  0.01  foot,  and  also  to  the  nearest  %-inch;  mark  the 
latter  on  the  stakes  for  the  information  of  the  ditcher,  using 
waterproof  keel  and  plain  numerals;  make  estimate  of  the 
quantity  of  drain  pipe,  and  of  the  cost  of  the  job.  Follow 
the  accompanying  forms. 


PROBLEMS. 


81 


' 

(PROF 

LE    LI 

YZL    H 

ores, 

GROUN: 

ELEVATIOMS    TO  O.I  FOOT.) 

109 

7/sis 

S.o 

713.3 

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I/O 

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Re_d-  Grade  line-  elevations^  rates   of  grade. 
Blue.  Wafer  level;  notes  fe/af,'ve  to  ^sarne. 
BtocK.  Syrface   fine,   stcrt/on  numerals, 


220 


82  THE   LEVEL 


PROBLEM  C4.  RAILROAD  PROFILE  LEVELING. 

(a)  Equipment. — Engineers'  leveling  instrument,  leveling 
rod,  100-foot  steel  tape,  stakes,  axe. 

(b)  Problem-.— Run.  levels   over   a   short  section  of   line 
staked  out  after  the  manner  of  railroad  surveys,  for  the 
purpose  of  constructing  a  profile. 

(c)  Methods. — Follow  the  general  process  outlined  in  the 
preceding  problem,  taking  rod  readings  to  the  nearest  0.01 
foot  on  turning  points  and  bench  marks,  and  also  on  im- 
portant profiling  points,  when  consistent;   but  take  ground 
rod  readings  only  to  the  nearest  0.1  foot.     In  calculating 
elevations,  preserve  the  same  degree  of  exactness  in  the  re- 
sult as  observed  in  the  rod  reading,  that  is,  when  the  rod 
readings  are  taken   to  the   nearest  0.1   foot,  use  only   the 
nearest  0.1  foot  in  the  height  of  instrument  to  determine 
the  elevations.    When  a  hub  or  station  stake  is  to  be  used 
as  a  turning  point,  the  notes  should  show  the  ground  rod 
and  elevation  to  the  nearest  0.1  foot  on  the  line  preceding 
the  precise  turning  point  record.     Bench  marks  should  be 
selected1  with  reference  to  their  freedom  from  disturbance 
during  construction,  and  they  should  be  located  not  more 
than  1500  or  2000  feet  apart  along  the  line.    Check  levels  by 
the  same  parties  should  not  differ  more  than  0.05  foot  into 
the  square  foot  of  the  length  of  circuit  in  miles.    Back  and 
fore  sights  shoula  be  balanced,  and  no  sight  longer  than 
350  or  400  feet  should  be  taken.    In  order  to  secure  a  renre- 
sentative  profile,  ground  rods  should  be  taken  not  only  at 
every  station  stake,  but  also  at  every  important  chanee  of 
slope  between  station  points.     Pluses   may   be  determined 
either  by  pacing,  or  when  short,  by  means  of  the  leveling 
rod.     The   rodman    should   keen   a   record    of   the  turning 
points.     The  notes  should  be  checked  and  the  other  safe- 
guards taken,  as  outlined  in  the  practical  hints  under  the 
"Use  of  the  Level." 

The  profile  is  best  plotted  by  having  another  nerson  read 
off  the  data.  The  horizontal  scale  on  railroad  profiles  is 
usually  400  feet  to  the  inch  and  the  vertical  scale  20  feet  to 
the  inch.  Gradients  are  expressed  to  the  nearest  0.01  per 
cent.  It  is  usual  to  give  the  aliuement  notes  and  prominent 
topography,  as  shown. 


PROBLEMS. 


S3 


PROBLEM  C5.  VERTICAL  CURVE. 

(a)  h'liiiiiiniciit.— Drafting  instruments,  profile  paper. 

(b)  Problem. — Connect  two    grade   lines   by    a   parabolic 
curve,  as  assigned. 

(c)  Methods.— (1)  Plot  the  given  grade  lines,  station  num- 


•  */. 
i •  07.00 


Ffate,  r=  o.SO  per  *t 
Length,  L  =  £=  10. 


Chord  Gradients. 


9S 


COMPARISON      OF    RESULTS. 


of  Grade 
Tangent. 


BY  Tangent  Correct 
Tangent        Cu 


— FT" 

+  O.OO 
i-0.  fO 
+  O.4O 
-f-0.  90 
•f-  /•  60 
+  2.  SO 
+  I-6O 
+  0.90 
-1-0.  40 
+  O-/0 
+  0-00 


Ft. 
/  07.  OO 

i06.ro 

'OS.  40 
'04.90 
'04-60 
/O4-50 
f04.60 
/  O4-00 


By  Chord  Gradients. 
Chord  Gradient.  Curve 
Di-ff.  Gradient.  Elevation 


Per  Cent. 


Per  Cenf. 
(-1.00) 
-0.90 
-O.7O 
-Q.SO 
-0.30 
-0.  I  0 

-f-o./o 

+  0.30 
i-0.  SO 
+  O.7O 
+0.90 
(+1.00) 


/  OS.  00 
I 07.OO 
I  06  OO 

tos.oo 

104.00 
/O3.OO 

toz.oo 

IO3-OO 
1 04.00 

tos.oo 

t06.00 
/07.OO 
/  08-OO 


107.  OO 

foe.to 

105-40 


/06.10 
I  07.0O 


f04  60 
/04.SO 
f04.60 
/Of.  90 
'OS-40 
106.  >0 
107.00 


84  THE  LEVEL. 

bers,  etc.,  on  the  sheet  of  profile  paper.  (2)  Determine  the 
grade  angle,  that  is,  the  algebraic  sum  of  the  two  rates  of 
grade.  (3)  Determine  the  length  of  the  vertical  curve  by 
dividing  the  grade  angle  by  the  assigned  or  adopted  change 
of  grade  per  station  (notice  the  analogy  to  simple  circular 
curves).  (4)  Calculate  the  apex  correction.  (5)  Determine 
the  corrections  at  the  several  station  or  fractional  stations 
(as  assigned),  and  tabulate  the  stations  and  elevations,  (.fi) 
Plot  the  vertical  curve  from  the  data  so  determined,  as  in 
the  example.  (7)  Also  compute  and  plot  the  same  curve  by 
the  method  of  chord  gradients. 

PROBLEM  C6.  ESTABLISHING  A  GRADE  LINE. 

(a)  Equipment. — Leveling  instrument,  leveling   rod,   flag 
pole,  100-foot  steel  tape,  stakes,  axe. 

(b)  Problem. — Establish  an  assigned  grade  line,    (1)   by 
measured  distances  and  calculate  rod  readings,  and  (2)  by 
"shooting  in"  the  same  line,  for  comparison. 

(c)  Method*— (I)  Stake  off  the  distance  between  ruling 
points,  and  drive  stakes  to  the  required  grade,  or  if  desira- 
ble, parallel  to  it,  by  dividing  up  the  fall  in  proportion  to 
the  distance,     (2)  Set  the  level  over  one  ruling  point  and 
determine  the  height  from  the  point  to  the  line  of  collima- 
tion  by  means  of  the  leveling  rod;  set  the  flag  pole  behind 
the  other  ruling  point  and  establish  a  target,  consisting  of  a 
rubber  band  holding  a  strip  of  paper  wrapped  about  the 
pole  at  a  height  equal  to  the  rod  reading;  having  thus  con- 
structed a  line  parallel  to  the  d'esired  grade  line,  direct  the 
telescope  on  the  fore  sight  target,  and  with  the  same  rod 
reading,  "shoot  in"  the  same  stakes.     Make  careful  record 
of  data  and  comparative  results. 

PROBLEM  07.  SURVEY  OF  LINE  SHAFTING. 

(a)  Equipment—  Engineers'  transit  with  attached  bubble, 
leveling  rod  (or  instead  of  these  engineers'  instruments,  a 
16-foot  metal-bound  straight-edge  with  an  adjustable  bubble 
of  say  20-foot  radius,  a  long  braided  fishing  line,  and  3  long 
metal  suspenders  exactly  alike  (as  shown  in  the  form),  to 
suspend  straight-edge  from  line  of  shafting).  2  good  plumb 
bobs,  50-foot  etched  steel  tape,  copper  tacks,  hatchet. 

(b)  Problem.— Make  a  survey  of  a  line  of  shafting  in  a 


PROBLEMS. 


machine  shop,  and  establish  a  true  alinement  for  it,  both 
vertically  and  transversely. 

(c)  Mftliwl*.—  (Assuming  that  the  transit  and  rod  are 
not  available),  (1)  Plan  the  survey  carefully,  and  if  possi- 
ble find  some  well  denned  base  line  close  to  the  line  shaft- 
ing, to  which  to  refer  its  position  transversely.  (2)  Stretch 
the  braided  string  from  end  to  end  of  the  shaft  line  (or  from 
end  to  end  of  the  room  in  case  the  shafting  passes  through 
the  wall),  and  fix  it  taut  on  or  parallel  to  the  adopted  base 
of  reference;  upon  finally  fixing  the  location  of  the  string, 
at  least  three  points,  one  at  either  end  and  one  near  the 
middle  of  its  length,  should  be  carefully  plumbed  down  and 
marked  temporarily  with  copper  tacks  in  the  wooden  floor 
of  the  shop  for  further  reference;  there  should  be  as  little 
draft  as  possible  during  this  and  the  following  steps.  (3) 
Plumb  down  from  the  line  shaft  at  each  hanger  and  care- 
fully measure  the  horizontal  right  angled  distance  to  the 
reference  string,  noting  the  nearest  1-16-inch;  the  hangers 
should  be  numbered  and  the  distances  between  them  meas- 
ured and  recorded;  the  plumb  bob  should  be  suspended  from 
corresponding  points  at  all  the  hangers;  and  the  bob  should 
always  hang  from  the  same  side  of  the  shafting;  likewise, 
the  shafting  should  be  calibrated,  and  record  made  of  any 
changes  of  diameter  found.  (4)  Determine  the  radius  of 
curvature  of  the  bubble  on  the  straight-edge,  (the  radius 
should  be  at  least  20  feet);  test  the  parallelism  of  the  edge 
of  the  straight-edge  and  the  bubble  line  after  the  manner 
used  with  the  carpenters'  level,  that  is,  by  reversion,  and 


Resurve 


j, Meta)    Shop. 


86  THE  LEVEL. 

adjust  the  bubble  if  found  in  error;  or  if  there  is  no  way  to 
adjust  the  bubble,  find  its  mean  position.  (5)  Prove  the 
equality  of  the  suspenders  in  a  similar  manner,  by  hanging 
them  from  the  shafting  and  testing  them  with  the  adjusted 
straight-edge.  (6)  Having  verified  the  special  instruments, 
determine  the  relative  elevations  of  the  shafting  at  the  suc- 
cessive hangers,  noting  the  nearest  1-16-inch  of  elevation; 
the  differences  can  be  accurately  measured  by  means  of  a 
wedge  scale;  for  greater  precision,  the  level  may  be  reversed 
end  for  end  each  time,  and  the  mean  taken;  reduce  the 
level  notes  by  summing  up  the  differences  algebraically  so 
as  to  secure  elevations  relative  to  the  first  or  any  other 
hanger  as  a  reference  or  bench,  or  above  or  below  any 
datum  plane  desired;  it  is  a  good  plan  to  adopt  a  marked 
spot  on  a  machine  or  engine  foundation  as  zero  datum.  (7) 
Plot  the  data  on  profile  paper,  so  as  to  secure  an  exagger- 
ated vertical  and  lateral  profile;  now  inspect  the  several 
hangers  and  note  the  margin  of  adjustment  available  in  the 
screws,  making  record  of  same  on  the  profile;  if  the  line  of 
shafting  passes  through  into  another  room  of  the  shop, 
carry  a  line  through  a  door  or  other  opening  on  the  pro- 
longation of  the  reference  line,  using  great  care  with  the 
parallels,  if  any  be  required;  collect  complete  data  rela- 
tive to  the  alinement  through  the  length  of  the  entire 
shafting,  as  described  above  for  the  first  stretch  of  it;  also 
plot  any  definite  lines  such  as  jack  shafting  lines  or  axes  of 
long  or  important  machines  which  may  now  or  in  the  future 
bear  a  relation  to  the  shafting  now  under  survey.  (8) 
Study  the  profiles  very  carefully  with  the  aid  of  a  fine 
thread;  and  after  due  consideration  of  all  ruling  points  and 
conditions,  lay  a  line  on  it  with  a  view  to  secure  the  best 
results  with  the  least  disturbance  of  the  shafting;  abrupt 
turns  or  elbows  are  likely  where  shafting  passes  through 
small  openings  in  partition  walls,  and  sudden  swings  often 
occur  near  heavy  machines;  the  ideal  alineruent  is  a  hori- 
zontal right  line;  if  only  slight  changes  are  required,  they 
may  be  made  at  once,  but  if  the  readjustments  are  con- 
siderable in  amount,  it  may  be  wise  to  check  up  the  main 
lines  of  the  survey  before  disturbing  the  hangers;  after  es- 
tablishing the  lines,  it  is  best  to  fix  permanent  reference 
points  for  future  use,  and  these  points  should  be  character- 
istic (such  as  one  copper  tack  surrounded  by  three  others), 


PROBLE.  13.  87 

to  avoid  mistakes  of  identification;  a  line  of  tacks,  one  be- 
neath the  edge  of  each  hanger,  located  say  in  a  vertical 
plane  tangent  to  the  same  side  of  the  shafting  throughout, 
establishes  the  element  of  the  cylinder,  which  is  more  con- 
venient to  use  than  the  axis  of  the  shaft  line.  (9)  Care- 
fully preserve  the  record  of  the  survey  and  changes  of  the 
hangers,  and  in  due  time  make  a  resurvey  to  discover  loose 
and  shifting  hangers,  especially  near  belts  under  heavy 
stress. 

(Should  the  regular  engineers'  instruments  be  employed, 
the  general  method1  would  be  unchanged;  the  difference 
would  consist  in  the  greater  facility  of  securing  the  data, 
in  passing  through  difficult  places  from  one  room  of  the 
shop  to  another,  in  reestablishing  the  alinement,  and  in 
detecting  changes  subsequently.  As  a  rule,  the  resurvey 
should  be  made  when  the  shafting  is  idle,  and  if  a  transit 
or  level  is  employed,  it  should,  when  possible,  be  set  up  on 
a  masonry  foundation  of  an  engine  or  machine  to  aA'oid  dis- 
turbance from  the  shaky  wooden  floors  due  to  the  vibration 
of  machinery  elsewhere  in  the  shop,  or  to  the  observer  mov- 
ing about  the  tripod  legs.)  Keep  the  record  in  tabular 
form  and  make  profile  in  the  manner  indicated  in  the  ac- 
companying diagram. 

PROBLEM  C8.  CONTOUR  LEVELING. 

(a)  Equipment.— Engineers'  leveling  instrument,  leveling 
rod,  100-foot  steel  tape,  stakes,  axe. 

(b)  Problem. — Make  a  rapid  contour  survey  of  an  assigned 
tract  of  ground  with  the  level  and  chain. 

•  (c)  Method*. —  (1)  Examine  the  tract  and  plan  the  system 
of  reference  lines  for  locating  the  points  at  which  levels 
are  to  be  taken;  if  the  ground  is  comparatively  regular,  a 
simple  subdivision  into  squares  of  100  feet  may  suffice;  but 
if  much  broken,  special  lines  along  gullies  and  ridges 
should  be  included1  in  the  survey  plan.  (2)  Stake  off  the 
tract  according  to  the  plan,  and  make  a  record  of  the  same. 
(3)  Starting  from  an  assigned  bench,  determine  the  eleva- 
tions of  the  ground  at  the  various  stakes  and  at  such  other 
points  as  may  be  required  to  give  a  correct  basis  for  accu- 
rate contouring.  (4)  Plot  the  data,  and  interpolate  contours 
at  a  specified  interval,  employing  both  numerical  calcula- 


88 


THE  LEVEL 


Sully  f. 
*,*gt3 

an,  Y  3. 


CONTOUR    PLAT    AND    DEVICE   FOR  THE 
RAPID    INTERPOLATION    OF    CONTOURS. 


PROBLEMS.  89 

tions  and  geometrical  methods.     (5)  Finish  the  plat,  as  re- 
quired. 

PROBLEM  C9.  USE  OF  CONTOUR  MAP. 

(a)  Equipment. — Contour  map,  drafting  instruments,  etc. 

(b)  Problem. — From  the  given  contour  map:   (1)  construct 
profiles  on  the  assigned  lines;   (2)  project  a  line  of  specified 
grade  through  assigned  points  on  the  contour  map;   make 
profile,   lay  grade  line  and  estimate  earthwork   quantities 
approximately;  (3)  calculate  the  earthwork  quantities  from 
the  map  for  given  grade  planes  and  limitations  of  area. 
(The  third  step  may,  perhaps,  best  be  taken  with  a  different 
map  from  the  first  two.) 

(c)  Method*. —  (1)   Use  profile  paper  for  the  profiles.    (2) 
To  project  the  line  on  the   map,   set  the  dividers   at  the 
horizontal  distance  in  which  the  specified  gradient  will  sur- 
mount   the    vertical    interval    between    successive    contour 
planes;    then  beginning  at  a  specified  point,  locate  points 
on  the  successive  contour  lines  up  or  down  on  the  given 
gradient,  as  required;  sketch  in  the  route  roughly,  and  pro- 
ject a  series  of  connected  curved  and  tangent  lines  approxi- 
mating to  it;    construct  a  profile  along  the  new  line;    lay 
the  required  grade  line  on  the  profile,  and  estimate  approxi- 
mate  earthwork   quantities    for    specified    dimensions    and 
slopes  of  roadbed.     (3)  By  means  of  end  area  method  calcu- 
late   the    earthwork    quantities    required    to    establish    the 
specified  grade  planes  on  the  designated  contoured  area. 

PROBLEM  CIO.  TEST  OF  DELICACY  OF  BUBBLE  VIAL. 

(a)  Equipment. — Engineers'  leveling  instrument,  leveling 
rod,  tape,  level  tester. 

(b)  Problem. — Determine  the  radius  of  curvature  of  the 
assigned  bubble  vial.     (1)  by  means  of  the  optical  test,  and 
(2)  by  the  level  tester. 

(c)  Method*. — (1)  Measure  off  a  base  line  say  100  feet  long, 
set  level  at  one  end  and  hold  rod  on  a  peg  driven  at  the 
other  end;   note  the  target  movement  corresponding  to  a 
given  bubble  movement,  both  in  the  same  linear  unit;   cal- 
culate the  radius  by  the  method  shown  at  (h),  Fig.  18.     (2) 
Set  the  level  tester  on  a  solid  base  and  place  the  instru- 


90  THE  LEVEL. 

ment  on  it,  as  indicated  at  (i),  Fig.  18;  by  means  of  the 
micrometer  head  and  known  relations  of  the  level  tester, 
determine  the  angular  equivalent  in  seconds  for  one  divis- 
ion and  also  one  inch  movement  of  the  bubble,  from  which 
calculate  the  radius  of  curvature  of  the  vial  in  feet.  Follow 
the  form. 

PROBLEM  Gil.  COMPARISON  OF  LEVEL  TELESCOPES. 

(a)  Equipment. — Five  (or  other  specified  number)   engin- 
eers' levels  (both  wye  and  dumpy),  leveling  rod,  metallic 
tape. 

(b)  Problem. — Make  a  critical  examination  and  compari- 
son of  the  telescopes  of  the  assigned  instruments. 

(c)  Methods. — Carefully  read  the  discussion  of  the  tele- 
scope in  the  text.    Then  compare  the  telescopes  with  refer- 
ence to:     (1)  magnifying  power;   (2)  chromatic  aberration; 
(3)   spherical  aberration;    (4)   definition;    (5)   illumination; 
(6)  flatness  of  fields;   (7)  angular  width  of  field;   (8)  effect- 
ive aperture  of  objective.     Make  tabulated  record  of  com- 
parisons, giving  in  separate  columns;    (a)   locker  number; 
(b)    kind   of  level;    (c)    name  of   maker;    (d1)    magnifying 
power;  and  so  on  for  the  other  points  examined. 

PROBLEM   C12.    TESTS   OF   THE   WYE   LEVEL. 

(a)  Equipment.— Wye  level,  leveling  rod,  tape. 

(b)  Problem.— Test  the  essential  relations  and  adjustments 
of  the  wye  level. 

(c)  Methods.— Carefully  note  the  construction  of  the  as- 
signed level  and  the  positions  of  the  elementary  lines.  Then 
following  the  methods  outlined  in  the  text,   test  the   fol- 
lowing   adjustments    ('but    do    not    disturb    the    adjusting 
screws):     (1)  The  bubble,  both  as  to  the  azimuth  and  alti- 
tude movements;  find  the  position  of  the  bubble  when  par- 
allel to  the  element  of  the  rings.     (2)  The  line  of  collima- 
tion;  its  deviation  from  the  axis  in  400  feet.     (3)  The  wyes; 
finding  the  position  of  the  bubble  when  the  vertical  axis  is 
vertical.     Keep  a  neat  and  systematic  tabulated  record  of 
observed  numerical  data,  with  explanation  of  the  several 
adjustments. 


PROBLEMS. 


91 


PROBLEM   CIS.    ADJUSTMENT    OF   THE   WYE   LEVEL. 

(a)  Equipment— Wye   level    (reserved   expressly    for   ad- 
justment), leveling  rod,  tape,  adjusting  pin. 

(b)  Problem. — Make  the  full  series  of  adjustments  of  the 
wye  level. 

(c)  M cth mix—  Follow  the  methods  detailed  in  the  text  ac- 
cording to  the  following  program:      (1)   Adjust  the  bubble 
line  (a)   into  the  same  plane  with  the  bottom  element  of 
the  rings,  and  (b)  parallel  to  that  element.     (2)  Adjust  the 
line  of  collimation  to  coincide  with  the  axis  of  the  rings, 
first  on  a  long  distance;  and  then,  to  test  the  object  glass 
slide,  try  it  for  a  short  distance;    if  necessary,  shift  the 
reticule  in  rotation  to  make  the  horizontal  hair  horizontal, 
and  also  center  the  eyepiece.     (3)   Adjust  the  bubble  line 
perpendicular   to   the  vertical   axis   by   means   of  the   wye 
nuts.     (4)  Test  the  rings  of  the  wye  level  by  the  two-peg 
test;  if  the  level  has  a  reversion  bubble,  first  test  the  paral- 
lelism of  the  top  and  bottom  tangent  lines,  and  then  test 
the  rings.     Keep  a  clear  and  systematic  record.     In  each 
case,  state  (a)  the  desired  relation,  (b)  the  test,  and  (c)  the 
adjustment. 


92  THE  LEVEL. 

PROBLEM  C14.  SKETCHING  THE  WYE  LEVEL. 

(a)  Equipment.— Wye  level. 

(b)  Problem. — Make  a  first-class  freehand  sketch  of  the 
assigned  wye  level. 

(c)  Methods. — The  sketch  should  be  correct  in  proportion 
and  clear  in  detail.     The  essential  parts  should  be  desig- 
nated in  neat  and  draftsmanlike  form,  and  the  elementary 
lines  clearly  indicated. 

PROBLEM   CIS.   TESTS   OF   THE   DUMPY   LEVEL. 

(a)  Equipment. — Dumpy  level,  leveling  rod,  tape. 

(b)  Problem. — Test  the  essential  relations  and  adjustments 
of  the  dumpy  level. 

(c)  Methods. — Carefully  note  the  construction  of  the  as- 
signed level  and  the  position  of  the  elementary  lines.  Then, 
following  the  methods  outlined  in  the  text,  test  the  follow- 
ing adjustments:      (1)   the  bubble  line,  whether  perpendic- 
ular to  the  vertical  axis;    and  if  not,  what  is  the  angular 
inclination  of  the  vertical  axis  when  the  bubble  is  in  the 
middle?     (3)   The  line  of  collimation,  whether  parallel  to 
the  bubble  line.     Record  the  errors  and  observations  sys- 
tematically. 

PROBLEM  C16.  ADJUSTMENT  OF  THE  DUMPY  LEVEL. 

(a)  Equipment. — Dumpy  level  (reserved  expressly  for  ad- 
justment), leveling  rod,  tape,  pegs,  axe,  adjusting  pin. 

(b)  Problem.— Make  the  essential  adjustments  of  the  as- 
signed dumpy  level. 

(c)  Methods. — (1)  Adjust  the  bubble  line  perpendicular  to 
the  vertical  axis.    (2)  Adjust  the  line  of  collimation  parallel 
to  the  bubble  line  by  the  two-peg  method.     In  describing 
the  adjustments,  the  record  should   state    (a)    the   desired 
relation,  (b)  the  test,  and  (c)  the  adjustment. 

PROBLEM   C17.   SKETCHING   THE   DUMPY   LEVEL. 
(See  Problem  C14.) 


PROBLEMS.  93 

PROBLEM    C18.    STRETCHING    CROSS-HAIRS. 

(a)  Equipment. — Engineers'  level  or  transit  (or  cross-hair 
reticule),  pocket  cross-hair  outfit,  reading  glass. 

(b)  Problem. — Renew  the  cross-hairs  in  a  level  or  transit 
instrument  by  a  method  applicable  to  field  use. 

(c)  Methods.— (It  instrument  is  provided,  follow  the  com- 
plete program   outlined   below;    otherwise,   merely   stretch 
the  lines  on  the  reticule  and  test  same.)     (1)  Remove  the 
eyepiece,   carefully  preserving  the  screws  from   loss.      (2) 
Remove  one  pair  of  the  capstan  headed   reticule  screws; 
turn  the -ring  edgewise  and  insert  a  sharpened  stick  in  the 
exposed  screw  hole,  take  out  the  other  two  screws  and  re- 
move reticule  from  telescope  tube.     (3)  Clean  the  cross-hair 
graduations,  and  support  the  reticule  on  a  sharpened  stick, 
or  (if  a  transit)  place  it  on  the  object  glass  with  a  piece  of 
paper  interposed  to  protect  the  lens.     (4)   Select  from  the 
capsule  (see  (d),  Fig.  17)  two  spider  lines  2  inches  or  more 
long,  and  fasten  a  stick  to  either  end  of  each  hair  by  means 
of  glue  from  the  adhesive  paper.     (5)  Put  the  hairs  in  place, 
(with  the  bits  of  wood  hanging  loose),  shifting  them   as 
desired  with  a  pin  point  or  knife  blade.     (6)  Apply  a  bit  of 
the  moistened  adhesive  paper  to  the  reticule  over  each  hair, 
and  after  a  few  minutes  cut  or  break  the  sticks  loose.     (7) 
Test  the  hairs  by  blowing  on  them  full  force.     (8)  If  they 
stand  this  test,  replace  the  reticule,  and  adjust  the  instru- 
ment.   Make  a  record  of  the  process. 

PROBLEM  C19.  ERROR  OF  SETTING  A  LEVEL  TARGET. 

(a)  Equipment. — Engineers'  leveling  instrument,  leveling 
rod  (perferably  a  New  York  or  Boston  rod),  tape,  pegs. 

(b)  Problem. — Determine  the  probable  error  of  setting  the 
level  target  at  distances  of  100  and  300  feet  (or  such  other 
distances  as  may  be  assigned. 

(c)  Method*.— (I)  Determine  the  magnifying  power  of  the 
telescope.      (2)    Determine   the   radius  of  curvature  of  the 
level  vial  by  the  field  method.     (3)  Determine  the  space  on 
the  rod-covered  by  the  diameter  of  the  hair.     (4)  Drive  a 
peg  at  ICO  feet  from  the  level,  level  up,  and  secure  ten  satis- 
factory consecutive  rod  readings  with  rod  held  truly  plumb 
on  the  peg;   shift  the  target  several  inches  between  read- 


94  THE  LEVEL. 

ings,  and  reset  without  bias;  reject  no  readings;  watch  the 
bubble  closely,  but  work  briskly.  (4)  Repeat  the  series  at 
300  feet.  (5)  Determine  for  each  distance  the  mean  rod, 
the  probable  error  of  a  single  reading,  and  of  the  mean,  as 
indicated  in  the  form, 


PROBLEM  C20.  COMPARISON  OF   DIFFERENT   MAKES 
AND  TYPES   OF   ENGINEERS'   LEVELS. 

(a)  EtiniiniH'iit. — Department  equipment,  catalogs  of  repre- 
sentative engineering  instrument  makers. 

(b)  PrvMcin. — Make  a  critical  comparison  of  the  several 
types  and  makes  of  engineers'  levels. 

(c)  MrtJiat]*.— Examine   the   department   equipment   and 
study  the  several  catalogs  carefully,  noting  the  usual  and 
special  features,  prices,  etc.,  and  prepare  a  systematic  sum- 
mary or  digest  of  the  same.    Prepare  brief  specifications  for 
a  leveling  instrument,  and  also  suggest  the  preferred  make. 


CHAPTER  V. 
THE  TRANSIT. 


Description.— The  engineers'  transit  consists  of  an  ali- 
dade, carrying  the  line  of  sight,  attached  to  an  inner  verti- 
cal spindle  (or  upper  motion)  which  turns  in  an  cuter  an- 
nular spindle  (or  lower  motion).  The  latter  carries  the 
horizontal  graduated  circle  or  limb,  and  is  supported  by  the 
tripod  head.  The  alidade  includes  the  telescope,  magnetic 
needle  with  its  graduated  circle,  and  the  vernier;  it  may  be 
revolved  while  the  graduated  limb  remains  stationary.  The 
horizontal  limb  is  graduated  to  degrees  and  half  degrees 
and  sometimes  to  twenty  minutes,  and  is  numbered  prefer- 
ably from  zero  to  360°  in  both  directions. 

The  complete  transit  differs  from  the  plain  transit,  Fig. 
20,  in  having  a  vertical  arc  and  level  bubble  attached  to 
the  telescope. 


COMPLETE     TRANSIT.  PLAIN    TRANSIT. 

Fig.  20. 


96 


THE   TRANSIT. 


In  Fig.  21  are  shown:  (a)  the  English  theodolite;  (b) 
the  shifting  plates  and  foot  screws  of  a  transit;  (c)  the 
Saegmuller  solar  attachment  to  the  transit;  (d)  the  grad- 


Fig.  21. 


USE  OF  THE  TRANSIT.  97 

ienter;  (e)  tripods;  (f)  reflectors;  (g)  reading  glass;  (h) 
flag  poles;  (i)  plumb  bobs;  (j)  the  Brunton  pocket  tran&it. 

The  Vernier. — The  vernier  is  an  auxiliary  scale  used  to 
read  fractional  parts  of  the  main  graduated  scale  or  limb. 
The  least  count  of  a  direct  vernier  is  found  by  dividing  the 
value  of  one  division  of  the  limb  by  the  number  of  divisions 
on  the  vernier.  With  a  limb  graduated  to  half  degrees  and 
a  direct  vernier  reading  to  single  minutes,  30  divisions  on 
the  vernier  cover  29  divisions  on  the  limb. 

In  read  in  <j  a  direct  vernier  observe  the  following  rule: 
Read  from  the  zero  of  the  limb  to  the  zero  of  the  vernier, 
then  along  on  the  vernier  until  coincident  lines  are  found. 
Add  the  reading  of  the  vernier  to  the  reading  of  the  limb. 

In  scttiny  the  vernier  to  a  given  reading,  as  for  example 
a  zero  reading  for  measuring  an  angle,  the  tangent  move- 
ment should  be  given  a  quick  short  motion  to  secure  the 
last  refinement,  since  a  slow  movement  is  not  noticed  by 
the  eye.  Notice  adjacent  and  end  graduations. 

In  Fig.  23,  (c)  is  a  vernier  reading  to  single  minutes,  (d) 
to  half  minutes  (30"),  and  (e)  to  thirds  of  minutes  (20"). 
The  slant  in  the  numerals  on  the  limb  corresponds  with  that 
on  the  vernier. 

USE  OF  THE  TRANSIT. 

Use.— The  complete  transit  is  used:  (1)  to  prolong  lines; 
(2)  to  measure  horizontal  angles;  (3)  to  measure  vertical 
angles;  (4)  to  run  levels;  (5)  to  establish  grade  lines.  The 
plain  transit  is  confined  to  the  first  two  uses,  unless  it  has  a 
vertical  clamp  and  tangent  movement,  when  it  may  be  used 
to  "shoot  in"  grade  lines. 

Prolongation  of  Lines. — If  the  instrument  is  in  adjust- 
ment a  line  can  be  prolonged  by  sighting  at  the  rear  sta- 
tion and  reversing  the  telescope  in  altitude.  It  is,  however, 
not  safe  to  depend  on  the  adjustments  of  the  transit,  and 
important  lines  should  always  be  prolonged  by  the  method 
of  "double  sights,"  as  given  in  Problem  D2.  Lines  may  be 
prolonged  with  the- plates  by  sighting  at  the  rear  station 
with  the  A  vernier  reading  180°,  reversing  the  alidade  in 
azimuth  and  locating  stations  ahead  with  the :  A  vernier 
reading  zero.  A  third  method  employs  two  points  ahead 
of  the  instrument. 


98  THE  TRANSIT. 

Measurement  of  Horizontal  Angles, -Horizontal 
angles  are  measured  as  described  in  Problem  Dl.  If  greater 
accuracy  is  required,  angles  may  be  measured  by  series  or 
by  repetition. 

By  Series.— In  measuring  an  angle  by  series  all  the 
angles  around  the  point  are  read  to  the  right,  both  verniers 
being  read  to  eliminate  eccentricity.  The  instrument  is 
then  reversed  in  altitude  and  azimuth  and  all  the  angles 
around  the  point  are  read  to  the  left.  The  readings  are 
checked  by  sighting  back  on  the  first  point  in  each  case. 
These  observations  constitute  one  "set."  The  vernier  is 
shifted  between  sets  360°  divided  by  the  number  of  sets. 
The  arithmetical  mean  of  the  observed  values  is  taken  as 
the  true  value. 

Bit  Repetition. — Angles  are  measured  by  repetition  as 
described  in  Problem  DIG.  This  method  is  especially  suited 
to  the  accurate  measurement  of  angles  with  an  ordinary 
transit  and  is  to  be  preferred  to  the  series  method  which  is 
a  favorite  where  precise  instruments  are  used.  In  the  repe- 
tition method  all  the  instrumental  errors  are  eliminated 
and  the  error  of  reading  is  very  much  reduced.  It  is  doubt- 
ful if  it  is  ever  consistent  to  make  more  than  5  or  6  repe- 
titions. 

Azimnth.— The  azimuth  of  a  line  is  the  horizontal  angle 
which  it  makes  with  a  line  of  reference  through  one  of  its 
ends,  the  angles  being  measured  to  the  right  from  0°  to 
360°,  as  in  (f)  Fig.  23.  It  is  usual  to  assume  that  the  true 
meridian  is  the  line  of  reference,  the  north  point  being 
taken  as  zero  in  common  surveying. 

Deflection. — The  deflection  of  a  line  is  the  angle  that  it 
makes  with  the  preceding  line  produced,  and  is  called  de- 
flection right  or  left  depending  upon  whether  the  angle  is 
on  the  right  or  left  side  of  the  line  produced,  as  in  (h)( 
Fig.  23. 

Vertical  Angles.— Vertical  angles  are  referred  to  the 
horizon  determined  by  the  plane  of  the  level  under  the 
telescope,  and  are  angles  of  depression  or  elevation  relative 
to  that  plane.  In  measuring  vertical  angles/the  instrument 
should  be  leveled  by  means  of  the  level  under  the  telescope 
and  correction  should  be  made  for  index  error  of  the- ver- 
nier. With  a  transit  having  a  complete  vertical  circle,  the 
true  vertical  angle  may  be  obtained  by  measuring  the 


USE  OF  THE  TRANSIT.  99 

angle  with  the  telescope  normal  and  reversed  and  taking 
the  mean. 

Traversing.— A  traverse  is  a  series  of  lines  whose 
lengths  and  relative  directions  are  known.  Traverses  are 
used  in  determining  areas,  locating  highways,  railroads,  etc. 

Azimuth  Traverse.— In  an  azimuth  traverse  the  azi- 
muths of  the  lines  are  determined,  usually  passing  around 
the  field  to  the  right.  In  <,r\ni1\n<i  the  transit  at  any  station 
the  A  vernier  is  set  to  read  the  azimuth  of  the  preceding 
course,  the  telescope  is  reversed,  directed  towards  the  pre- 
ceding station  and  the  lower  motion  clamped;  the  telescope 
is  then  reversed  in  altitude.  The  reading  of  the  A  vernier 
with  telescope  normal  will  then  give  the  azimuth  of  any  line 
sighted  on.  If  there  is  any  error  in  collimation  the  transit 
may  be  oriented  by  sighting  back  with  the  A  vernier  read- 
ing the  back  azimuth  of  the  preceding  course.  In  a  closed 
traverse  the  last  front  azimuth  should  agree  with  the  first 
back  azimuth.  The  azimuth  traverse  is  especially  adapted 
to  stadia  and  railroad  work.  Azimuths  can  be  easily 
changed  to  bearings,  if  desired. 

Deflection  Traverse. — In  a  deflection  traverse  the  de- 
flection of  each  line  is  determined,  usually  passing  around 
the  field  to  the  right.  To  avoid  discrepancies  due  to  error 
in  collimation,  the  transit  may  be  oriented  by  sighting  at 
the  preceding  station  with  the  A  vernier  set  at  180°,  the 
telescope  being  in  its  normal  position,  and  the  lower  mo- 
tion clamped.  The  reading  of  tae  A  vernier  will  then  give 
the  deflection  of  any  line  sighted  on. 

Compass  Bearings. — Compass  bearings  should  always 
be  read  on  an  extended  traverse  as  a  check  against  such 
errors  as  using  the  wrong  motion  or  an  erroneous  reading 
of  the  vernier.  To  guard  against  errors  due  to  local  attrac- 
tion, back  and  front  bearings  should  always  be  read,  and 
the  angle  thus  determined  compared  with  the  transit  angle. 

Leveling  with  the  Transit.— The  transit  with  an  at- 
tached level  is  the  complete  equivalent  for  the  engineers' 
level.  The  instrument  is  leveled  up  with  the  plate  levels 
first,  after  which  the  position  of  the  attached  bubble  is  eon- 
trolled  by  means  of  the  vertical  tangent  'movement. 

Grade  Lines. — Grade  lines  may  be  established  with  the 
transit  either  by  means  of  known  distances  and  calculated 
rod  readings,  or  by  "shooting  in"  a  parallel  line  by  means 


100  THE  TRANSIT. 

of  the  inclined  telescope,  as  deserioed  under  the  use  of  the 
engineers'  level.  For  the  latter  purpose  the  transit  is  rather 
more  convenient  than  the  level. 

Setting  up  the  Transit.— To  set  the  transit  over  a  point 
spread  the  legs  so  that  they  will  make  an  angle  of  about 
30°,  place  them  symmetrically  about  the  point  with  two  logs 
down  hill.  Bring  one  plate  level  parallel  to  two  of  the  legs, 
force  these  legs  firmly  into  the  ground  and  bring  the  plumb 
bob  over  the  point  and  the  plates  approximately  level  with 
the  third  leg,  changing  the  position  of  the  plumb  bob  with 
a  radial  motion  and  leveling  the  plates  with  a  circular  mo- 
tion of  the  leg.  Finish  the  centering  with  the  shifting 
plates.  In  leveling  up  the  bubbles  move  with  the  left  thumb. 
Use  care  to  bring  the  foot  screws  to  a  proper  bearing. 

Parallax.— Before  beginning  the  observations  the  eye- 
piece should  be  carefully  focused  on  the  cross-hairs  so  as  to 
prevent  parallax. 

Back  Sight  With  Transit.— A hcays  check  the  Itncl-  xifiJtt 
tefore  moving  the  transit  to  see  that  the  instrument  has  not 
been  disturbed  or  that  a  wrong  motion  has  not  been  used. 

Instrumental  Errors. — The  transit  should  be  kept  in  as 
perfect  adjustment  as  possible,  and  should  be  used  habitual- 
ly as  though  it  were  out  of  adjustment,  that  is,  so  that  the 
instrumental  errors  will  balance.  No  opportunity  should  be 
lost  to  test  adjustments. 

ADJUSTMENTS  OF  THE  TRANSIT. 


Elementary  Lines. — Fig.  22  shows  the  elementary  lines 
of  the  transit,  viz.,  (1)  line  of  collimation;  (2)  horizontal 
axis;  (3)  vertical  axis;  (4)  plate  level  lines;  (5)  attached 
level  line.  These  lines  should,have  the  following  relations: 
(a)  the  plate  levels  should  be  perpendicular  to  the  vertical 
axis;  (b)  the  line  of  collimation  should  be  perpendicular  to 
the  horizontal  axis;  (c)  the  horizontal  axis  should  be  per- 
pendicular to  the  vertical  axis;  (d)  the  attached  level  line 
should  be  parallel  to  the  line  of  collimation.  The  following 
additional  relations  should  exist:  (e)  the  vertical  axes  of 
the  upper  and  lower  motions  should  be  coincident;  (f)  the 
optical  center  of  the  objective  should  be  projected  in  the 
line  of  collimation;  (g)  the  center  of  the  graduated  circle 


ADJUSTMENT  CF  THE  TRANSIT 


101 


should  be  the  center  of  rotation,  i.  e.,  there  should  be  no 
eccentricity. 

Plate  Levels. — To  make  the  ]>l<itc  7rn7.s-  in'ri>ciidit-nlar  to  the 
vertical  axis. — Make  the  vertical  a.rlx  vertical  tni'l  adjuxt  tin1 
bubbles  to  the  middle  of  their  race.  The  vertical  axis  is  made 
vertical  by  leveling  up,  reversing  in  azimuth,  and  if  the 
bubbles  move,  bring  them  half  way  back  with  the  foot 
screws.  The  adjustment  is  the  same  as  for  the  compass,  and 
the  reasons  are  shown  in  (a),  Fig.  13. 

After  adjusting  the  plate  levels  with  reference  to  say  the 
upper  motion,  test  them  with  the  lower  motion  to  prove 
the  coincidence  of  the  vertical  axes. 

Line  of  Collimation.— To  make  the  line  of  collimation  per- 
pendicular to  the  horizontal  axis. — Construct  a  straight  tine 


Fig.  22. 


102  THE  TRANSIT. 

and  adjust  the  vertical  liair  so  that  the  instrument  Kill 
in  altitude  on  it.  The  straight  line  may  be  established  either 
by  prolongation  beyond  a  point  in  front,  or  preferably  by 
the  methods  of  double  sighting,  described  in  Problem  D2. 
One-fourth  the  apparent  error  is  corrected  for  the  reasons 
indicated  in  (a),  Fig.  23.  In  deciding  which  way  to  move 
the  hair,  notice  that  the  optical  center  is  the  fulcrum.  The 
transit  should  be  collimated  first  for  equal  back  and  fore 
sights,  say  100  feet  or  so,  and  then  checked  for  a  dis- 
tant point  in  one  direction  and  perhaps  50  feet  in  the  other, 
so  as  to  test  the  motion  of  the  optical  center  of  the 
objective.  The  points  should  all  be  as  definite  as  possible. 
Chaining  pins  may  be  used,  or  V-marks  may  be  made  on  the 
side  of  a  stake  driven  securely.  Each  altitude  reversal 
should  be  checked  back  and  forth  to  make  sure  of  the  pro- 
longations, and  the  telescope  should  be  handled  very  care- 
fully. If  the  cross-hair  reticule  is  removed  from  the  instru- 
ment or  should  be  much  disturbed,  the  foregoing  adjustment 
is  made  approximately  and  the  hair  is  made  vertical  by  sight- 
ing on  a  plumb  line,  such  as  the  corner  of  a  building,  or  by 
noting  whether  the  hair  continuously  covers  the  same  point 
as  the  telescope  is  moved  in  altitude;  the  collimation  ad- 
justment is  then  made  precisely. 

Horizontal  Axis. — To  make  the  horizontal  axis  perpen- 
dicular to  the  vertical  axis.— Adjust  the  horizontal  a.ris  so 
that  the  line  of  collimation  icill  follow  a  plumb  line.  An  actual 
plumb  line  may  be  used;  or  preferably  a  vertical  line  may  be 
constructed  by  first  sighting  on  a  high  point,  then  depres- 
sing the  telescope  and  marking  a  low  point;  then  reversing 
in  altitude  and  azimuth  (turning  the  horizontal  axis  end  for 
end),  sighting  at  the  high  point  again  and  marking  a  second 
low  point  beside  the  first  one.  The  mean  of  the  two  low 
points  is  vertically  beneath  the  upper  one.  The  transverse 
plate  level  is  especially  important  in  this  process.  One  end 
of  the  horizontal  axis  is  changed,  as  in  (b),  Fig.  23. 

Attached  Level. — To  make  the  attached  level  and  the  line 
of  collimation  parallel  to  each  other.— Construct  a  level  line  and 
adjust  the  instrument  to  agree  with  it.  The  level  line  may  be 
obtained  either  by  using  the  surface  of  a  still  body  of  water, 
as  of  a  pond,  or  it  may  be  constructed  by  equal  back  and 
fore  sights,  as  indicated  in  (e),  Fig.  16.  Either  the  horizon- 
tal hair  may  be  changed  to  bring  the  line  of  collimation 


ADJUSTMENT  OF  THE  TRANSIT.  103 


(C) 


(dr 


Fig.  23. 


parallel  to  the  bubble  line,  or  vice  versa.  The  method  is  the 
same  as  used  for  the  dumpy  level. 

If  the  bubble  vial  is  a  reversion  level,  as  shown  at 
(b),  Fig.  18,  tihe  adjustment  is  much  simpler.  However,  the 
two-peg  test  should  be  applied  at  least  once  to  the  reversion 
level  to  prove  the  parallelism  of  the  top  and  bottom  tangent 
lines  of  the  bubble  vial. 

Vertical  Arc.— After  the  last  preceding  adjustment,  the 
vernier  of  the  vertical  circle  should  be  made  to  read  zero 
when  the  bubble  is  at  the  center  of  the  tube.  Bring  the 
bubble  to  the  center  and  shift  the  vernier  to  read  zero.  If 
the  vernier  is  fixed,  an  index  correction  may  be  applied  to 
all  vertical  angles;  or  the  bubble  may  be  made  to  agree 
with  the  vernier  and  the  horizontal  hair  then  adjusted  by 
the  two-peg  method. 


104  THE  TRANSIT. 

Eccentricity.— Read  the  two  verniers  at  intervals  around 
the  circle;  if  the  verniers  have  changed  the  same  amount  in 
each  case  the  circle  is  well  centered.  If  the  two  verniers 
have  not  changed  the  same  amount,  the  mean  of  the  angles 
passed  over  by  the  verniers  is  the  actual  angle  through 
which  the  instrument  has  turned.  The  error  cannot  be  ad- 
justed. 

Centering  the  Eyepiece.— If  the  intersection  of  the 
cross-hairs  is  not  in  the  center  of  the  field  of  view,  move  the 
inner  ring  of  the  eyepiece  slide  by  means  of  the  screws 
which  hold  it. 

PROBLEMS  WITH  THE  TRANSIT. 

PROBLEM  Dl.    ANGLES  OF  A  TRIANGLE  WITH  TRAN- 
SIT. 

(a)  Equipment. — Transit,  2  flag  poles,  reading-glass. 

(b)  Problem.— Measure  the  angles  of  a  given  triangle  vith 
the  transit. 

(c)  Methods. — (1)  Set  the  transit  over  one  of  the  vertices 
of  the  triangle  and  plumb  a  transit  pole  over  each  of  the 
other  two.     (2)  Set  the  A  vernier  to  read  zero,  sight  at  the 
left  hand  point  approximately,  clamp  the  lower  motion  and 
make  an  exact  bisection  with  the  lower  tangent  movement. 
(3)   Unclamp  the  upper  motion,   sight  at  the  right  hand 
point  approximately  and  make  an  exact  bisection  with  the 
upper  tangent  movement.     (4)   Read  the  A  vernier  to  the 
nearest  single  minute.    This  reading  is  the  angle  sought.  (5) 
With  the  A  vernier  set  to  read  zero  repeat  the  measurement, 
sighting  first  at  the  right  hand  station  and  then  at  the  left. 
The  recorded  value  of  the  angle  is  to  be  the  mean  of  these 
two  determinations  which  must  not  differ  by  more  than 
one  minute.     (6)  Measure  the  other  angles  in  like  n:anner. 
The  error  of  closure  must  not  exceed  one  minute.     Follow 
the  prescribed  form. 

PROBLEM   D2.     PROLONGATION    OF    A    LINE     WITH 
TRANSIT. 

(a)  Equipment.— Transit,  2  flag  poles,  axe,  6  hubs,  6  flat 
stakes,  tacks. 


PROBLEMS. 


105 


Station 
'  > 


(b)  Problem. — Prolong  a  EOD-foot    base    line    successively 
with  the  transit  by  the  method  of  "double  sights"  about 
1500  feet,  and  check  on  a  hub  previously  established. 

(c)  Methods.— (1)  Drive  two  hubs,  A  and  B,  about  1500  feet 
apart.     (2)  Set  the  transit  over  tack  in  hub  A,  sight  at  flag 
pole  plumbed  over  tack  in  hub  B,  drive  hub  C  about  SCO 
feet  from  the  transit  and  locate,  a  tack  in  line  very  care- 
fully.   Remove  the  flag  pole  from  hub  B.     (3)  Set  the  tran- 
sit over  hub  C,  back  sight  on  hub  A  and  clamp  the  vertical 
axis.     (4)  Reverse  the  telescope,  drive  hub  D  at  a  distance 
of  about  300  feet  and  mark  line  very  carefully  with  a  pen- 
cil.    (5)  Reverse  the  transit  in  azimuth,  sight  on  hub  A;  re- 
verse the  telescope  and  locate  a  second  point  on  hub  D. 
Drive  a  tack  midway  between  these  two  points.     (6)  Set  the 
transit  over  the  mean  point  on  hub  D,  back  sight  on  hub 
C,  prolong  300  feet  and  set  hub  E  by  double  sights.     (7)  Set 
over  hub  E,  back  sight  on  hub  D,  prolong  300  feet  and  set 
hub  P,  as  before.     (8)   Finally  prolong  from  hub  F,  with 
back  sight  on  E,  and  establish  mean  tack  at  terminal  hub 
B.     Record  the  collimation  errors  at  D,   E,  and  the  final 
error  at  B.    Follow  the  form. 


106.  THE  TRANSIT. 

PROBLEM  D3.     INTERSECTION  OF  TWO  LINES  WITH 
TRANSIT. 

(a)  Equipment.— Transit,  2  flag  poles,  plumb  line  string, 
axe,  6  hubs,  6  flat  stakes,  tacks. 

(b)  Problem—  Determine  the  intersection  of  two  lines  with 
the  transit. 

(c)  Methods. — (1)  Set  the  transit  over  a  hub  and  tight  at  a 
second  point  on  line.    (2)  Set  and  tack  a  hub  on  line  a  short 
distance  on  each  side  of  the  intersection.    (3)  Set  the  trans- 
sit  over  a  hub  on  the  second  line  and  sight  at  a  point  on 
line.    (4)  Locate  a  hub  at  the  intersection  by  sighting  with 
the  transit  and  stretching  a  string  between  the  two  hubs 
located  on  the  first  line.     (5)  Measure  the  angle  of  inter- 
section.   Record  the  data. 

PROBLEM  D4.    TRIANGULATION  ACROSS  A  RIVER. 

(a)  Equipment. — Transit,     2    flag    poles,     100-foot    steel 
tape,  axe,  4  hubs,  4  flat  stakes,  tacks. 

(b)  Problem.— Determine  the  distance  across  an  imaginary 
-river  by  triangulating  with  the  transit  and  check  by  direct 

measurement. 

(c)  Methods. — (1)  Set  the  transit  over  a  hub  on  line  on  one 
bank,  and  set  a  hub  on  the  opposite  bank  of  an  imaginary 
river  about  800  feet  wide  by  "double  sigths".     (2)  Turn  off 
90°  and  lay  off  a  base  line  very  carefully  with  the  steel  tape. 
(3)  Set  the  transit  over  the  hub  at  the  farther  end  of  the 
base  line  and  measure  the  angle  between  the  lines  joining 
it  and  the  other  points.     (4)  Compute  the  distance  across 
the  river.     (5)  Measure  the  distance  across  the  rive."  and 
compare  with  the  computed  distance.    The  difference  should 
not  be  greater  than  1:1000.    Follow  the  prescribed  form. 

PROBLEM  D5.     PASSING  AN  OBSTACLE  WITH  TRAN- 
SIT. 

(a)  Equipment.— Transit,  100-foot  steel  tape,  2  flag  poles, 
axe,  hubs,  flat  stakes,  tacks. 

(b)  Problem. — Prolong  a  line  beyond  an  imaginary  ob- 
stacle by  three  methods  and  check  by  direct  measurement. 

(c)  Methods.— (1)  Pass  the  obstacle  to  the  right  by  means 


PROBLEMS 


107 


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103  THE  TRANSIT. 

of  the  'equilateral  triangle  method"  with  sights  of  not  less 
than  2(TO  feet.  (2)  Pass  the  obstacle  to  the  right  by  means  of 
the  "right  angle  off-set  method"  and  check  on  the  same  hub 
as  before.  (3)  Pass  the  obstacle  to  the  left  by  means  of  the 
"deflection  method",  turning  off  an  angle  that  vrill  just 
pass  the  obstruction.  Check  the  three  methods  by  direct 
measurement.  Follow  the  prescribed  form, 

PROBLEM  D6.     TRAVERSE  OF  FIELD  WITH  TRANSIT. 

(a)  Equipment.— Transit,  2  Hag  poles,  100-foot  steel  tape. 

(b)  Prubh-m—  Determine  the  deflections  of  the  sides  of  an 
assigned  field  with  the  transit,  check  angles  by  observing 
the  magnetic  bearings,  and  measure  the  lengths  of  the  sides 
with  a  steel  tape. 

(c)  Methods. — (1)  Set  the  ti-ansit  over  one  corner  of  the 
field,  set  the  A  vernier  to  read  180°,  and  sight  at  a  flag 
pole  plumbed  over  the  point  to  the  left  with  the  telescope 
normal.    Read  and  record  the  magnetic  bearing.     (2)  Keep 
the  telescope  normal  and  sight  at  the  next  point  to  the  right. 
The  reading  of  the  A  vernier  will  be  the  deflection  of  the 
second   line.      (3)    Read   and   record  the  magnetic   bearing 
and  compare  the  transit  and  magnetic  deflections.     (4)  Re- 
peat this  process  for  the  remaining  corners  of  the  polygon 
taken  in  succession  to  the  right.    Deflections  will  be  based 
on   duplicate  readings   agreeing  within   one   minute.      (5) 
Measure  the  sides  to  the  nearest  0.01  foot  with  the  tape. 
Compare  the  tape  with  the  standard  at  the  beginning  and 
conclusion  of  the  chaining.     (6)  From  the  observed  deflec- 
tions determine  the  bearings  of  the  field  assuming  one  side 
as  a  true  meridian.    The  angular  error  of  closure  must  not 
exceed  one  minute.    Record  and  reduce  data  as  in  the  pre- 
scribed form. 

PROBLEM  D7.     AREA  OF  FIELD  WITH  TRANSIT. 

(a)  Equipment.— Five-place  table  of  logarithms. 

(b)  Proft/em.— Compute  the  area  of  the  assigned  field  by 
means  of  latitudes  and  departures. 

(c)  Methods.— (I)    Prepare    forms    for    calculation;    tran- 
scribe data,  and  carefully  verify  copy.     (2)  Compute  lati- 
tudes and  departures  by  contracted  multiplication,  preserv- 


PROBLEMS. 


109 


110  THE  TRANSIT. 

ing  results  to  the  nearest  0.01  foot.  (3)  Make  the  same  cal- 
culations by  logarithms  as  a  check.  (4)  Determine  the  ac- 
tual linear  error  of  closure.  (4)  Determine  the  permissible 
error  of  closure  .(see  chapter  on  errors  of  suveying).  (6)  If 
consistent,  distribute  the  errors  in  proportion  to  the  several 
latitudes  and  departures,  respectively,  repeating  the  addi- 
tions as  a  check.  (7)  Copy  the  field  notes  and  adjusted  lati- 
tudes and  departures,  and  verify  transcript.  (8)  Calculate 
the  meridian  distances  of  the  several  stations  and  lines.  (9) 
Calculate  the  latitude  coordinates.  (10)  Calculate  the  par- 
tial trapezoidal  areas  by  multiplying  the  meridian  dis- 
tances of  the  lines  by  the  respective  latitudes,  preserving 
consistent  accuracy,  and'  observing  algebraic  signs.  (11) 
Determine  the  area  by  taking  the  algebraic  sum  of  the 
partial  areas.  Reduce  to  acres,  preserving  results  to  the 
nearest  0.001  acre.  Follow  the  prescribed  forms. 

PROBLEM  D8.     STAKING  OUT  A  BUILDING. 

(a)  Equipment.— Transit,  100-foot  steel  tape,  2  flag  poles, 
axe,  hubs,  tacks,  plan  of  building. 

(b)  Probltm. — On  an  assigned  plot  of  ground  stake  out 
the  assigned  building. 

(c)  Methods. — (1)    Orient  one  side  of  the  enclosing  rec- 
tangle with  reference  to  a  true  meridian  or  a  street  line.  (2) 
Locate  and  check  up  the  corners  of  the  rectangle,  by  set- 
ting over  each  corner  in  turn,  passing  around  to  the  right, 
back-sighting  on   the  corner  to  the   left,   turning   off   90° 
and  locating  the  corner  to  the  right.    (3)  Locate  the  corners 
of  the  building  by  setting  stakes  on  the  side  lines  of  the 
building  produced,  using  the  rectangle  as  a  base  line.     (4) 
Check  all  stakes  by  additional  measurements.  The  rectangle 
should  close  to  the  nearest  minute,  the  linear  error  should 
not  exceed  1:50,000.    Follow  the  prescribed  form. 

PROBLEM   D9.     HEIGHT  OF  TOWER  WITH   TRANSIT. 

(a)  Equipment. — Complete  transit,  2   flag  poles,  leveling 
rod,  100-foot  steel  tape,  axe.  hubs,  tacks. 

(b)  Problem. — Determine  the  height  of  an  assigned  tower 
with  the  transit  and  steel  tape. 

(c)  Methods.—  (1)  Set  the  transit  over  a  hub  located  a  little 


PROBLEMS. 


Ill 


112  THE  TRANSIT. 

further  from  the  base  than  the  height  of  the  lower.  (2) 
Level  the  instrument  very  carefully  with  the  attached  level 
and  determine  the  index  error  of  the  vertical  circle.  (3) 
Bring  the  bubble  of  the  attached  level  to  the  center  and  read 
a  level  rod  held  on  the  base  of  the  tower.  (4)  Sight  at  the 
top  of  the  tower,  read  the  vertical  angle,  correct  for  index 
error  and  record.  (5)  Reverse  the  telescope  and  locate  a 
second  point  at  least  as  far  from  the  first  as  the  height  of 
the  tower,  check  by  "double  sights."  (6)  Set  the  transit 
over  the  second  hub,  sight  at  the  top  of  the  tower  and  read 
the  vertical  angle,  as  before.  (7)  Read  the  level  rod  on  the 
base  of  the  tower  as  before.  Each  angle  and  rod  reading 
is  to  be  based  on  duplicate  readings.  Follow  the  prescribed 
form. 

PROBLEM   DID.    ANGLES   OF   TRIANGLE    BY   REPETI- 
TION. 

(a)  Equipment. — Transit,  reading  glass,  2  chaining  pins, 
2  tripods  with  plumb  bobs  (if  necessary). 

(b)  Problem-. — Measure  the  angles  of  a  prescribed  triangle 
with  transit  by  repetition. 

(c)  .l/r/7/of/s.— (l)Set  the  transit  over  one  of  the  vertices  of 
the  triangle  and  set  chaining  pins  in  the  tops  of  the  monu- 
ments at  the  other  two.     (2)  Set  the  A  vernier  to  read  zero, 
(3)   Sight  at  the  left  hand  station  with  the  bubble  down, 
and  clamp  the  lower  motion.     (4)  Unclamp  the  upper  mo- 
tion, sight  at  the  right  hand  station,  read  both  verniers  and 
record.     (5)   Unclamp  the  lower  motion,  sight  at  the  left 
hand  station,  and  check  the  verniers  to  see  that  they  have 
not  moved.     (6)  Unclamp  the  upper  motion  and  sight  at  the 
right  hand  station  but  do  not  read  verniers.     Repeat  until 
five  repetitions  of  the  angle  are  secured,  and  read  both  ver- 
niers to  eliminate  errors   of  eccentricity.      (7)    Divide  the 
arithmetrical  mean  of  the  two  vernier  readings  by  five  and 
compare  with  the  value  obtained  by  single  measurement.  (8) 
Reverse  the  instrument  in  altitude,  and  set  the  A  vernier  to 
read  zero.     (9)   Sight  at  the  right  hand  station  with  the 
bubble  up,  and  clamp  the  lower  motion.     (10)  Unclamp  the 
upper  motion,- sight  art- the  left  hand  station,  read  both  ver- 
niers and  record.     (11)  Unclamp  the  lower  motion,  sight  at 
the  right  hand  station,  and  check  the  verniers  to  see  that 


PROBLEMS. 


113 


ANCLfS      OF 


TRIAN  iLE      S 


114.  THE  TRANSIT. 

they  have  not  moved.  (12)  Unclamp  the  upper  motion  and 
sight  at  the  left  hand  station,  but  do  not  read  the  verniers. 
Repeat  until  five  repetitions  of  the  angle  are  secured,  and 
read  both  verniers  to  eliminate  errors  of  eccentricity.  (13) 
Divide  the  mean  of  the  two  vernier  readings  by  five  and 
compare  with  the  value  obtained  by  single  measurement 
(14)  Take  the  mean  of  the  two  sets  as  the  most  probable 
value.  (15)  Measure  the  other  angles  in  the  same  manner. 
The  angular  error  of  closure  should  not  exceed  15".  Follow 
the  prescribed  form. 

PROBLEM  Dll.  DETERMINATION  OF  TRUE  MERIDIAN 
BY  OBSERVATION  ON  POLARIS  AT  ELONGATION. 

(a)  Equipment. — Complete  transit,   reading  glass,   hub,   2 
flat  stakes,  plank  18"x  4"x  2",  4  8d  nails,  axe,  2  lanterns, 
good  watch  set  and  regulated  to  keep  railroad  time. 

(b)  Problem.— Determine  a  true  meridian  by  an  observa- 
tion on  Polaris  at  elongation. 

(c)  Methods. — (1)    Calculate   the    time   of   elongation   of 
Polaris,  and  regulate  and  set  a  good  reliable  watch  to  keep 
railroad  time  (mean  solar  time  for  the  90th  meridian.)     (2) 
Set  the  transit  over  a  hub  about  40  minutes  before  the  time 
of  elongation.     (3)Level  the  instrument  very  carefully,  and 
set  the  vernier  of  the  vertical  circle  to  read  the  latitude  of 
the  place.     (2)  Focus  the  objective  on  a  bright  star;  sight 
at  Polaris  which  will  be  found  by  following  the  pointers  of 
the  Great  Dipper  at  an  elevation  equal  to  the  latitude  of  the 
place.     (3)  With  a  reflector  or  a  piece  of  white  paper  re- 
flect light  into  the  telescope  so  that  the  cross-hairs  and  the 
image  of  Polaris  will  be  visible  at  the  same  time.     (4)  De- 
press the  telescope  and  establish  a  target  at  a  distance  of 
about  500  feet;  place  the  plank  on  the  ground  and  nail  it 
firmly  to  a  flat  stake  driving  one  at  each  end.  (5)  Level  up 
again  and  follow  Polaris  with  the  telescope  by  means  of  the 
tangent  movement;  at  elongation  it  will  appear  to  traverse 
the  vertical  hair  for  several  minutes.     (6)  Depress  the  tele- 
scope, sight  at  a  pencil  held  on  the  target  and  mark  the 
noint  very  carefully.     (7)  As  a  check  make  three  observa- 
tions within  half  an  hour  after  elongation,  noting  the  time 
of  sighting  on  the  star.    Reverse  the  instrument  in  altitude 
nnd  azimuth  after  the  first  check  observation.     (8)  Reduce 
the  check  observations  to  observations  at  elongation  by  the 


PROBLEMS. 


115 


following  rule:  Multiply  the  square  of  the  time  since 
elongation  in  minutes  by  0.058,  and  the  product  will  be  the 
correction  to  the  azimuth  of  Polaris  in  seconds  of  arc,  for 
latitude  40°.  (9)  The  next  morning  lay  off  the  azimuth  of 
Polaris  for  each  observation  to  the  east  or  west  depending 
upon  whether  the  observation  was  made  at  western  or  east- 
ern elongation.  (10)  Check  the  observed  meridian  with  the 
standard  meridian.  The  error  of  the  mean  of  the  four  ob- 
servation should  not  exceed  one  minute.  Record  and  re- 
duce the  data  as  in  the  prescribed  form. 

PROBLEM  D12.  DETERMINATION  OF  TRUE  MERIDIAN 
BY  OBSERVATION   ON  POLARIS   AT   ANY  TIME. 

(a)  Equipment. — The  same  as  in  Dll. 

(b)  Problem. — Determine   a  true   meridian   by   observing 
Polaris  at  any  time. 

(c)  MethndK.—  (l)   Make  the  observations  in  the  manner 
described  in  Dll.     (2)  Compute  the  azimuth  of  Polaris  at 
the  time  of  each  observation,  using  the  tables  given  in  the 
U.  S.  Land  Survey  Manual,  pp.  118-119;  Johnsons'  Survey- 
ing, pp.  814-815;   Wilsons'  Topographic  Surveying,  pp.  716- 


116 


THE  TRANSIT. 


AZIMUTHS  OF  POLARIS  AT  ELONGATION 

Between  1900  and  1910  and  Latitudes 3O  and6o°North. 

(From  U.  S.  Land  Survey  Manvil.) 


Latit»de. 

1900. 

1901. 

1902. 

1903. 

1904. 

»9°5- 

30 

I  24.9 

i  24.6 

i  24.2 

i  23.9 

i  23.5 

I    23.1 

31 

25.8 

25-5 

25-1 

24-7 

24.4 

24.0 

32 

26.7 

26.4 

26.0 

25.6 

25-3 

24.9 

33 

27-7 

27.3 

27.0 

26.6 

26.2 

25.9 

34 

28.7 

28.4 

27.6 

27.2 

26.9 

35 

i  29.8 

i  29.4 

I   29.0 

l  28.7 

i  28.3 

I    27-9 

36 

30.9 

30.5 

30.1 

29.8 

29.4 

29.0 

37 

32.1 

3i-7 

31-3 

30,9 

30.5 

30.1 

38 

33-4 

33-0 

32.6 

32.2 

31.  s 

31.4 

39 

34-7 

34-3 

33-9 

33-5 

33-1 

32.7 

40 

i  36.0 

i  35-6 

i  35.2 

I  34.8 

i  34-4 

I  34-0 

41 

37-5 

37-1 

36.7 

36.2 

35-8     ;         35-4 

42 
43 

39-o 
40.6 

38/6 
40.2 

38.2 
39-8 

37-7 
39-3 

37-3             36.9 
38-9             38.5 

44 

42.3 

41-8 

41.4 

41.0 

40.5             40.1 

45 

I  44.0 

I  43-6 

I  43-2 

i  42-7 

I  42.3          i  41.8 

46 

45-9 

45-5 

45.0 

44-6 

44.2             43.7 

47 

47-9 

47-4 

46.9 

46.5 

46.0      ;           45.6 

48 

49-9 

49-5 

49-o 

48.6 

48.1               47.7 

49 

52.1 

51-7 

51.2 

50.7 

50.2               49.8 

50 

I  54-4 

I  54.0 

i  53-5 

i  53-0 

1    52.5           I    52.0 

Latitude. 

1906. 

1907. 

1908. 

1909. 

,9,0. 

3° 

I   22.8 

i  22.4 

I    22.1 

I   21-7 

I   21.3 

31 

23.6 

23.2 

22.9 

22.5 

22.2 

32 

24-5 

24.1 

23.8 

23-4 

23.1 

33 

25-5 

25-1 

24-7 

24.3 

24.0 

34 

26.5 

26.1 

25-7 

25-3 

25.0 

35 

I  27.5 

i  27.1 

I    26.8 

I   26.4 

I    26.0 

36 

28.6 

28.2 

27.9 

27-5 

27.1 

37 

29.7 

29.3 

29-0 

28.6 

28.2 

38 

31.0 

30.6 

30.2 

29.8 

29.4 

39- 

32.3 

31-8 

31-4 

31-0 

30.6 

40 

I  33-6 

I  33-2 

I    32-8 

I  32.4 

I    32.0 

41 

35-0 

34.6 

34-2 

33-8 

33-4 

42 

36.5 

36.0 

35-6 

35-2 

34-8 

43 

38. 

37-6 

37-2 

36.8 

36.3 

44 

39- 

39-2 

38.8 

33.4 

37-9 

45 

I  41. 

I  40.9 

I  40.5 

I  40.1 

I  39-6 

46 

43- 

42.7 

42.3 

41.9 

41.4 

47 

45- 

44-6 

44-2 

43-7 

43-3 

48 

47- 

46.7 

46.3 

45-8 

45-3 

49 

49- 

48.4 

47  -9 

47-4 

50 

i  51- 

I  51-0 

i  50.6 

i  50.1 

I  49-6 

PROBLEMS. 


117 


CORRECTION  TO  AZIMUTHS  OF  POLARIS  FOR  EACH   MONTH. 
(From  U.  S.  Land  Surrey  Manual.) 


Latitude. 

Latitude. 

•f. 

40°. 

55°- 

35°. 

40*. 

55°. 

January.... 

' 

-  0.4 

-0.5 

July  

,    Q 

+  0.3 

+     -4 

February  .  .  . 

—  °-3 

—  0.3 

-  0.4 

August  

~\~  °- 

-4-  o.  I 

+      -2 

March  
April  

—  O.I 

—  0.2 

—  0.2 

September.  . 

0. 
—  0. 

—  0.  I 

-  o-3 

—     -4 

May  
June  

+  0.2 

+  0.3 

+  0.4 

December..  . 

—  0. 

-  o.S 

-     -7 

LOCAL  MEAN  TIME-OF  UPPER  CULMINATION  OF  POLARIS. 

Computed  for  Longitude  6  hours  or  90°  W.  of  Greenwich. 

(From  U.  S.  Land  Survey  Manual.) 


Date. 

1900 

,,0, 

190*. 

,„. 

.904. 

1903. 

Dift.  for 
i  Day. 

Jan. 

Feb. 

I 
Mar. 

Apr. 

636.3 
5  4i-o 
433-9 
3  38.6 
2  43.4 
148.2 

6  37.4 
5  42-1 
4  35-o 
3  39-7 
2  44.5 
i  49-3 

638.5 
5  43-2 
436.1 
340.8 
2  45-6 
i  50.4 

039.6 
5  44-3 
4  37-2 
341-9 
246-7 
I  51-5 

6  40.7 
545-4 
438.3 
3  43-0 
2  47-8 
I  52.6 

641.8 
546.5 
4  39-4 
344-1 
2  48.9 
i  53-7 
046.8 

3-95 
3-95 
3-95 
3-95 
3  94 
3-94 
3-94 

May' 

3  42-4 
239-5 

22  40.6 

22  41.7 

242.8 

346.8 

2  43.9 

23  47-9 
22  44.0 

3-93 
3-93 

June 
I 
July 

Aug. 
i 
Sept. 

Oct. 

i 

o  38.0 
943-2 
8405 
7  45-7 
6  39.1 
5  44-3 
4  37-6 
342.7 
2  39.9 
i  44  9 

20  39.1 
9  44-3 
8  41.6 
746.8 
6  40.2 
545-4 
4  38.7 
343-8 
2  41.0 
I  46.0 

20  40.2 

9  45-4 
8  42.7 
7  47-9 
641-3 
5  46-5 
4  39-8 
3  44-9 
2  42.1 
I  47-1 

041.3 
946.5 
843.8 
7  49-0 
6  42.4 
547.6 
4  0.9 
3  6.0 
2  3.2 
I  8.2 

042.4 
9  476 
8  44.9 
7  50.1 
6  43.5 
5  48-7 
4  42.0 
3  47-1 
2  44-3 
I  49-3 

2043-5 
19  48.7 
1  8  46.0 
17  5L2 
16  44.6 
15  49-8 
I443.I 
13  48.2 
12  45.4 
II   50.4 

3  92 
3-92 
3-92 
3-92 
3  9  1 
3-92 
3-92 
3.92 
3-93 
3-93 

I 
Dec. 
15 

9  42-9 
8  399 
7  44-7 

9  44-0 
8  41.0 

7  45-8 

9  45-1 
842.1 
7  46.9 

9  6.2 
8  3.2 
7  48.0 

9  47-3 
844.3 
7  49-1 

948.4 

8  45-4 
7  502 

3-94 
3-94 
3.94 

118  THE  TRANSIT. 

717.  (3)  The  next  morning  lay  off  the  computed  azimuth 
for  each  observation.  (4)  Check  the  observed  meridian 
with  the  standard  meridian.  The  error  of  the  mean  of  the 
five  observations  should  not  exceed  one  minute.  Record 
the  data. 

PROBLEM     D13.     COMPARISON     OF     TRANSIT     TELE- 
SCOPES. 

(a)  Equipment. — Five  engineers'  transits. 

(b)  Problem.— .Make  a  critical  comparison  of  the  telescopes 
of  five  engineers'  transits. 

(c)  Methods. — Follow  the  methods  outlined  in  the  com- 
parison of  level  telescopes. 

PROBLEM  D14.  TEST  OF  A  TRANSIT. 

(a)  Equipment. — Transit,     reading    glass,    leveling    rod, 
chaining  pins,  foot  rule. 

(b)  Problem. — Test  the  following  adjustments  of  an  as- 
signed transit:     (1)   Test  the  graduation  for  eccentricity 
(2)  Test  the  plate  levels  to  see  if  they  are  perpendicular  to 
the  vertical  axis.     (3)  Test  the  line  of  collimation  to  see  if 
it  is  perpendicular  to   the  horizontal  axis.     (4)    Test   the 
horizontal  axis  to  see  if  it  is  perpendicular  to  the  vertical 
axis.     (5)  Test  the  level  under  the  telescope  to  see  if  the 
tangent  to  the  tube  at  the  center  is  parallel  to  the  line  of 
collimation.    (6)  Test  the  vertical  circle  to  see  if  the  vernier 
reads  zero  when  the  line  of  sight  is  horizontal. 

(c)  Methods. — Make  the  tests  as  described  in  the  first  part 
of  this  chapter  but  do  not  make  any  of  the  adjustments  or 
tamper  with  any  of  the  parts  of  the  instrument.    Check  each 
test.     Make  a  careful  record  of  the  methods  and  errors,  in- 
cluding a  statement  of  the  manner  of  doing  correct  work 
with  each  adjustment  out. 

PROBLEM  D15.   ADJUSTMENT   OF  A   TRANSIT. 

(a)  Equipment. — Transit,  reading  glass,  leveling  rod, 
chaining  pins,  adjusting  pin,  small  screw  driver. 

(c)  Methods.— Make  the  following  tests  and  adjustments 
of  an  assigned  transit  that  has  been  thrown  out  of  adjust- 
ment by  the  instructor:  (1)  Test  the  graduation  for  eccen- 


PROBLEMS. 


119 


tricity.  (2)  Adjust  the  plate  levels  perpendicular  to  the 
vertical  axis.  (3)  Adjust  the  line  of  collimation  perpendicu- 
lar to  the  vertical  axis.  (4)  Adjust  the  horizontal  axis  per- 
pendicular to  the  vertical  axis.  (5)  Adjust  the  level  under 
the  telescope  parallel  to  the  line  of  collimation.  (6)  Ad- 
just the  zero  of  the  vertical  circle  to  read  zero  when  the 
line  of  sight  is  horizontal.  (7)  Center  the  eyepiece. 

(c)  Methnds.—Ma.'ke  the  tests  and  adjustments  as  de- 
scribed in  the  first  part  of  this  chapter.  Use  extreme  care 
in  manipulating  the  screws  and  if  any  of  the  parts 
stick  or  work  harshly,  call  the  instructor's  attention  before 
proceeding.  Repeat  the  tests  and  adjustments.  Make  a 
careful  record  of  methods  and  errors. 

PROBLEM   D16.   SKETCHING   A   TRANSIT. 

(a)  I-'<ii(ii»mcnt. — Engineers'  transit. 

(b)  Problem.— Make  a  first-class  sketch  of  an  engineers' 
transit. 

(c)  Methods. — (See  similar  problem  with  the  level.) 


The  floff  iv<a 
'rpf&feat  /vsf 
Error 


'ftfof     eacn  fr'fnt. 
TO  ft. 

00  Ft. 

+r-^°3j£  ,0,103 *>. 
4/0?-  0.031  In-aoon ft 


-10.  006J- 


120  THE  TRANSIT. 

PROBLEM  D17.  ERROR  OF  SETTING  FLAG  POLE  WITH 
TRANSIT. 

(a)  Equipment. — Transit,  iron  flag  pole,  flat  stake  l"x  2"x 
15",  foot  rule. 

(to)  Problem. — Determine  the  probable  error  of  setting  a 
flag  pole  with  the  transit  at  a  distance  of  300  feet.  Repeat 
for  600  feet. 

(c)  Methods—  (1)  Set  the  transit  up  and  sight  at  the  flag 
pole  plumbed  near  the  middle  of  the  stake  at  a  distance  of 
about  300  feet.  (2)  Measure  the  distance  from  the  point  of 
the  flag  pole  to  a  mark  on  the  stake.  (3)  Keep  the  vertical 
axis  clamped,  and  move  the  pole  to  one  side.  (4)  Set  the 
pole  with  the  transit,  and  measure  the  distance  from  the 
first  line.  (5)  Repeat  until  at  least  ten  consecutive  satis- 
factory results  are  obtained.  (6)  Compute  the  probable 
error  of  a  single  observation  and  of  the  mean  of  all  the 
observations  (see  chapter  on  errors  of  surveying),  and  re- 
duce the  mean  error  to  its  angular  value.  (7)  Repeat  for  600 
feet.  Determine  distances  by  pacing.  Follow  the  prescribed 
form. 

PROBLEM  D18.  REPORT  ON  DIFFERENT  MAKES  AND 
AND  TYPES   OF   TRANSITS. 

(a)  Equipment.— Department  equipment,  catalogs    of    the 
principal  makers  of  engineers'  transits. 

(b)  Problem. — Make  a  critical  comparison  of  the  several 
types  of  transits  made  by  the  different  makers. 

(c)  Methods.— (See  similar  problem  with  the  level.) 


CHAPTER  VI. 
TOPOGRAPHIC  SURVEYING. 


Topographic  Map.— A  topographic  map  is  one  which 
shows  with  practical  accuracy  all  the  drainage,  culture,  and 
relief  features  that  the  scale  of  the  map  will  permit.  These 
features  may  be  grouped  under  three  heads  as  follows:  (1) 
the  culture,  or  features  constructed  by  man,  as  cities,,  vil- 
lages, roads;  (2)  the  hypsography,  or  relief  of  surface  forms, 
as  hills,  valleys,  plains;  (3)  the  hydrography,  or  water 
features,  as  ponds,  streams,  lakes.  The  culture  is  usually 
represented  by  conventional  symbols.  The  surface  forms 
are  shown  by  contours  (lines  of  equal  height),  (a)  Fig.  24, 
or  hachures,  (b)  Fig.  24.  The  water  features  are  shown  by 
soundings,  conventional  signs  for  bars,  etc. 

Topographic  maps  may  be  divided  into  two  classes  de- 
pending upon  the  scale  of  the  map.  Small  scale  topographic 
maps  are  made  by  the  U.  S.  Coast  and  Geodetic  Survey  and 
the  U.  S.  Geological  Survey,  and  are  drawn  to  a  scale  of 
1:62,500,  1:125,000  or  1:250,000  with  corresponding  contour 
intervals  of  5  to  50,  10  to  100,  and  200  to  250  feet.  These 
maps  show  the  streams,  highways,  railroads,  canals,  etc.,  in 
outline  but  do  not  show  any  features  of  a  temporary  char- 
acter. 


Fig.  24. 


122  TOPOGRAPHIC  SURVEYING. 

Large  scale  topographic  maps  are  drawn  to  a  scale  of  400 
feet  to  1  inch  (1:4800),  or  greater,  with  contour  intervals 
from  1  to  10  feet  depending  upon  whether  the  ground  is  flat 
or  hilly.  Roads,  streets,  dwellings,  streams,  etc.,  are  drawn 
to  scale.  Features  too  small  to  be  properly  represented 
when  drawn  to  scale  are  drawn  out  of  proportion  to  the 
scale  of  the  map. 

Topographic  Survey. — The  object  of  a  topographic  sur- 
vey is  the  production  of  a  topographic  map,  and  hence 
neither  time  nor  money  should  be  wastefully  expended  in 
obtaining  field  data  more  refined  than  the  needs  of  the  map- 
ping demand. 

METHODS. — A  topographic  survey  may  be  dividied  into 
three  parts:  (1)  the  reconnaissance;  (2)  the  skeleton  of 
the  survey;  (3)  filling  in  the  details. 

Reconnaissance. — The  reconnaissance  is  a  rapid  prelim- 
inary survey  to  determine  the  best  methods  to  use  in  mak- 
ing the  survey  and  the  location  of  the  principal  points  of 
control.  A  careful  reconnaissance  enables  the  topographer 
to  choose  methods  that  are  certain  to  result  in  a  better  map 
and  a  distinct  saving  of  time. 

Skeleton. — There  are  three  general  methods  of  locating 
the  skeleton  of  a  topographic  survey:  (1)  tie  line  survey 
with  chain  only;  (2)  traverse  method  with  transit  or  com- 
pass; (3)  triangulation  system,  (f),  Fig.  30.  The  first 
method  is  used  for  the  survey  of  small  tracts.  The  second 
method,  in  which  the  distances  are  measured  with  the  chain, 
tape  or  stadia,  is  used  on  railroad  and  similar  surveys.  The 
third  method,  in  which  triangulation  stations  are  connect- 
ed with  each  ether  and  with  a  carefully  measured  base  line 
and  base  of  verificatio'n,  is  used  on  surveys  for  small  scale 
maps  and  on  detailed  or  special  surveys,  such  as  surveys 
of  cities  and  reservoir  sites. 

Filling  in  Details.— There  are  three  general  methods 
employed  for  filling  in  details:  (1)  with  transit  or  compass 
and  chain;  (2)  with  transit  and  stadia;  (3)  with  plane  table 
and  stadia.  The  transit  and  stadia  are  used  by  the  Missis- 
sippi and  Missouri  River  Commissions.  The  plane  table 
and  stadia  are  used  by  the  U.  S.  Coast  and  Geodetic  and  the 
U.  S.  Geological  Surveys. 

Topographic  City  Survey.— A  topographic  city  survey  is 
one  of  the  best  examples  of  a  survey  for  a  large  scale  map. 


HYDROGRAPHIC    SURVEY.  123 

It  is  usually  based  on  a  system  of  triangulation  executed 
with  precision  and  connected  with  carefully  measured  base 
lines.  The  details  of  the  survey  are  usually  taken  up  in  the 
following  order:  (1)  reconnaissance  and  location  of  trian- 
gulation stations;  (2)  measurement  of  base  line  and  base  of 
verification;  (3)  measurement  of  angles  by  repetition;  (4) 
establishment  of  bench  marks  by  running  duplicate  levels, 
(5)  adjustment  of  angles  of  triangulation  system;  (6)  com- 
putation of  sides,  azimuths  and  coordinates;  (7)  filling  in 
details,  usually  with  transit  and  stadia;  (8)  plotting  of 
triangulation  and  other  important  points  on  the  map  by 
rectangular  coordinates;  (9)  plotting  the  details  and  com- 
pleting the  map.  The  instructions  given  on  the  succeeding 
pages  are  for  a  survey  of  this  type. 

HYDROGRAPHIC  SURVEY. 

Classes. — Hydrographic  surveying  may  be  divided  into 
river  and  marine.  The  first  includes  the  determination  of 
depths,  location  of  bars,  and  obstructions  to  navigation, 
determination  of  area  of  cross-section,  discharge,  sediment 
carried,  etc.  The  second  includes  the  making  of  soundings, 
location  of  bars,  ledges,  buoys,  etc.  The  depth  of  the  water 
is  determined  by  making  soundings  with  a  lead  or  rod, 
and  the  velocity  is  gaged  by  means  of  floats  or  a  current 
meter,  (d),  Fig.  31. 

Soundings  are  located:  (1)  by  two  angles  read  simulta- 
neously from  both  ends  of  a  line  on  the  shore,  (f),  Fig.  31; 
(2)  by  keeping  the  boat  in  line  with  two  flags  on  shore,  and 
determining  the  position  on  the  line  by  means  of  an  angle 
read  on  the  shore,  or  by  a  time  interval;  (3)  by  intersecting 
ranges,  (g),  Fig.  31;  (4)  by  stretching  a  rope  or  wire  across 
the  stream;  (5)  by  measuring  with  a  sextant  in  the  boat 
at  the  instant  that  the  sounding  is  taken  two  angles  to  three 
known  points  on  the  shore,  (c),  Fig.  31;  the  point  is  located 
by  solving  the  three  point  problem  graphically  with  the 
three  arm  protroctor,  (e),  Fig.  31;  (6)  by  locating  the  posi- 
tion of  the  boat  at  the  instant  that  the  soundings  are  taken 
with  transit  and  stadia.  The  first  three  methods  are  used 
on  small  river  or  lake  surveys.  The  fourth  method  is  used 
where  soundings  are  taken  at  frequent  intervals.  The  fifth 
method  has  been  used  almost  exclusively  in  locating  sound- 


124 


TOPOGRAPHIC  SURVEYING. 


ings  in  harbors,  lakes,  and  large  rivers.  The  sixth  method 
is  rapidly  coming  into  general  use  and  promises  to  be  the 
favorite  method. 

THE  STADIA. 

Description.— The  stadia  is  a  device  for  measuring  dis- 
tances by  reading  an  intercept  on  a  graduated  rod.  The 
stadia-hairs,  shown  in  (g),  Fig.  27,  are  carried  on  the  same 
reticule  as  the  cross-hairs  and  are  placed  equidistant 
from  the  horizontal  hair.  The  stadia-hairs  are  sometimes 
placed  on  a  separate  reticule  and  made  adjustable.  It  is, 
however,  considered  better  practice  by  most  engineers  to 
have  the  stadia-hairs  fixed  and  use  an  interval  factor, 
rather  than  try  to  space  the  hairs  to  suit  a  rod  or  to  gradu- 
ate a  rod  to  suit  an  interval  factor. 

Stadia  Rods. — Stadia  rods  are  always  of  the  self  reading 
type.  In  Fig.  27,  (a)  a-nd  (b)  are  the  kind  used  on  the  U.  S. 
Coast  Survey;  (c)  on  the  U.  S.  Lake  Survey;  (d)  and  (c)  by 
the  U.  S.  Engineers.  A  target  for  marking  on  the  rod  the 
height  of  the  horizontal  axis  of  the  transit  above  the  sta- 
tion occupied  is  shown  in  (f),  Fig.  27. 

Theory  of  the  Stadia. — In  Fig.  25,  by  the  principles  of 
optics,  rays  of  light  passing  from  points  A  and  B  on  the 
rod  through  the  objective  so  as  to  emerge  parallel  and  pass 
through  the  stadia-hairs  a  and  b,  respectively,  must  inter- 
sect at  the  principal  focal  point  d  in  front  of  the  objective; 
therefore  the  rod  intercept,  s  is  proportional  to  the  dis- 
tance, g  from  the  principal  focal  point  in  front  of  the  ob- 
jective. 


THE  STADIA. 


125 


Stadia  Formula  For  Horizontal  Line  of  Sight  and   Ver- 
tical Rod. — In  Fig.  25,  from  similar  triangles  we  have 


From  which 
and 


s  :g  ::  i  :  f 
g  =  -p  s  =  ks 
D  =  k  s  +  (c  -f  f) 


(1) 
(2) 
(3) 


Stadia   Formula   For  Inclined  Line  of  Sight  and  Ver- 
tical Rod— In  Fig.  26  we  have 


and 
but 


also 


BD  =  AE  cos  a                        (approx. )  (4) 

D  =  k  s  cos  a  +  (c  +  f)  (5) 

H  =  D  cos  a  (6) 

=  k  s  cos2  a  +  (c  +  f )  cos  a  (7 ) 

=  k  s  —  kssin2a  +  (c -f  f)  cos  a  (8) 

V  =  D  sin  a   .  (9) 

=  k  s  sin  a  cos  a  -f  (c  +  f)  sin  a  (10) 

,    ikssin2a  +  (c  +  f)  sin  a  (11) 


126 


TOPOGRAPHIC    SURVEYING. 


USE  OF  THE  STADIA.— The  transit  is  set  up  over  a 
station  of  known  elevation  and  with  a  given  direction  or 
azimuth  to  another  visible  station;  the  height  of  the  line  of 
collimation  above  the  top  of  the  station  is  determined  either 
by  holding  the  rod  beside  the  instrument  and  setting  the 
target,  or  preferably  by  graduating  one  leg  of  the  tripod 
and  using  the  plumb  bcb;  then  with  the  transit  oriented  on 
a  given  line,  "Phots"  are  taken  to  representative  points,  and 
record  made  of  the  rod  intercept,  vertical  angle  and  azi- 
muth. In  reading  the  intercept  the  middle  hair  is  first  set 
roughly  on  the  target,  then  one  stadia-hair  is  set  at  the 
nearest  foot-mark  on  the  rod  and  the  intercept  read  with 
the  other  stad'ia-hair,  after  which  the  precise  vertical  angle 
is  taken,  and  the  azimuth  is  read. 

Reducing  the  Notes. — The  notes  may  be  reduced  by 
means  of  tables,  diagrams,  or  a  special  slide  rule.  The  slide 
rule  is  the  most  rapid  but  has  the  disadvantage  that  it  can- 
not well  be  taken  into  the  field. 


Hi 


(0) 


<> 

'hi  (C)          (d) 

Fig.  27. 


«<! 


THE  PLANE  TABLE.  127 


1 1 
COMPLETE    PLANE  TABLES 


THE  PLANE  TABLE. 

Description. — The  plane  table  consists  of  an  alidade, 
carrying  a  line  of  sight  and  a  ruler  with  a  fiducial  edge.  The 
alidade  is  free  to  move  on  a  drawing  board  mounted  on  a 
tripod.  The  drawing  board  is  leveled  by  means  of  plate 
levels.  The  line  of  sight  should  make  a  fixed  horizontal 
angle  with  the  fiducial  edge  of  the  ruler.  The  complete 
plane  table  is  a  transit  in  which  the  horizontal  limb  has 
been  replaced  by  a  drawing  board. 

There  are  three  general  types  of  plane  tables:  (1)  the 
Coast  Survey  plane  table,  (a)  Fig.  28;  (2)  the  Johnson  plane 
table,  (b),  Fig.  28:  (3)  the  Gannet  plams  table,  (d),  Fig.  29. 

USE  OF  THE  PLANE  TABLE.— In  making  a  survey 
with  a  plane  table  the  angles  are  measured  graphically  and 
the  lines  and  points  are  plotted  in  the  field.  The  principal 
methods  of  making  a  survey  with  a  plane  table  are:  (1) 
radiation;  (2)  traversing;  (3)  intersection;  (4)  resection. 

Radiation. — In  this  method  a  convenient  point  on  the 
paper  is  set  over  a  selected  point  in  the  field,  and  the  table 
clamped.  The  line  of  sight  is  then  directed  towards  each 
point  to  be  located  in  turn  and  a  line  is  drawn  along  the 
fiducial  edge  of  the  ruler.  The  distances,  which  may  be  de- 
termined-by  measuring  with  chain,  tape  or  stadia,  are 
plotted  to  a  convenient  scale,  (a),  Fig.  30. 

Trarrr«ing. — This  method  is  practically  the  same  as  trav- 


128 


TOPOGRAPHIC  SURVEYING. 


Fig.  29. 

ersing  with  a  transit,,  (b),  Fig.  30.  Care  should  be  used 
in  orienting  the  plane  table  to  get  the  point  on  the  paper 
over  the  corresponding  point  on  the  ground  as  nearly  as  the 
character  of  the  work  requires. 

Intersection.— In  this  method  the  points  are  located  by  in- 
tersecting lines  drawn  from  the  ends  of  a  measured  base 
line,  (c),  Fig.  30. 

Resection.— In  the  resection  method  the  plane  table  is  set 
up  at  a  random  point  and  oriented  with  respect  to  either 
three  or  two  given  points,  which  gives  rise  to  two  methods 
known  respectively  as  the  three-point  and  two-point  prob- 
lems. 

Three  Point  Problem. — "Where  three  points  are  located  on 
the  map  and  are  visible  but  inaccessible,  the  plane  table  is 
oriented  by  solving  the  "three  point  problem".  There  are 
several  solutions,  the  'best  known  of  which  are:  (1)  the 
mechanical  solution;  (2)  the  Coast  Survey  solution;  (3) 
Bessel's  solution;  (4)  analytical  solution.  The  problem  is 
indeterminate  if  a  circle  can  be  passed  through  the  four 
points. 

In  the  mechanical  solution  the  two  angles  subtended  by 
the  three  points  are  plotted  graphically  on  a  piece  of  trac- 
ing paper  and  the  point  is  located  by  placing  the  tracing 
paper  over  the  plotted  points. 


THE   PLANE    TABLE. 


129 


In  Bessell's  solution,  (d),  Pig.  30,  a,  b,  c  are  three  points 
on  the  map  corresponding  to  the  three  points,  A,  B,  C  on 
the  ground,  and  D  is  the  randlom  point  at  the  instrument 
whose  location,  d,  it  is  desired  to  find  on  the  map.  Con- 
struct the  angle  1  with  vertex  at  point  c  as  follows:  Sight 
along  the  line  ca  at  the  point  C,  and  clamp  the  vertical  axis. 
Then  center  the  alidade  on  c  and  sight  at  B  by  moving  the 
alidade,  and  diraw  a.  line  along  the  edge  of  the  ruler.  Con- 
struct the  angle  2  with  vertex  at  a  in  the  siame  manner.  The 


Fig.  30. 


130  TOPOGRAPHIC  SURVEYING. 

line  joining  b  and  e  will  pass  through  the  point  d  required. 
Orient  the  board  by  sighting  at  B  with  the  line  of  sight 
along  the  line  e  b,  and  locate  d  by  resection. 

Two  Point  Problem.— To  orient  the  board  whon  only  two 
points  are  plotted,  proceed  as  follows:  Select  a  fourth 
point,  c,  that  is  visible,  and  with  these  two  points  as  the 
ends  of  a  base  line,  (e),  Fig.  30,  laid  off  to  a  convenient 
scale,  locate  two  points  a'  and  b'  on  the  map  by  intersec- 
tion. The  error  of  orienting  the  board  will  be  the  angle 
between  the  lines  a,  b  and  a'  b'.  The  table  can  now  be 
oriented  and  the  desired  point  located  on  the  board  by  re- 
section. 

Adjustments. — The  adjustments  of  the  plane  table  are: 
(1)  the  plate  levels;  (2)  the  line  of  collimation;  (3)  the 
horizontal  axis;  (4)  the  attached  level.  These  adjustments 
are  practically  the  same  as  those  for  the  transit. 

THE  SEXTANT. 

Description.— The  sextant  consists  of  an  arc  of  60°, 
with  each  half  degree  numbered  as  a  whole  degree,  (a),  Fig. 
31,  combined  with  mirrors  so  arranged  that  angles  can  be 
measured  to  120°. 

Theory. — The  principle  upon  which  the  sextant  is  con- 
structed is  that  if  a  ray  of  light  is  reflected  successively  be- 
tween two  plane  mirrors,  the  angle  between  the  first  and 
last  direction  of  the  ray  is  twice  the  angle  of  the  mirrors. 

In  (b),  Fig.  31,  the  angles  of  incidence  and  reflection 
are  equal, 

i  =  r  and  il  =  r1,  and 

E=  (i  +  r)  — (i1  +  r')=  2  (r-r>) 
Cl=  (90°  — i1)  — (90°— r)  =  (r  — r1) 
and  therefore    E  =  2  C1 

but  C1  =  angle  CIC1,  by  Geometry,    since  the 

mirrors  are  parallel  for  a  zero  reading. 

USE  OF  THE  SEXTANT.— To  measure  an  angle  be- 
tween two  objects  with  a  sextant  bring  its  plane  into  the 
plane  of  the  two  objects;  sight  at  the  fainter  object  with  the 
telescope  and  bring  the  two  images  into  coincidence.  The 


THE  SEXTANT. 


131 


Fig.  31. 


reading  is  the  angle  sought.  The  angle  will  not  be  the  true 
horizontal  angle  between  the  objects  unless  the  objects  are 
in  the  same  level  with  the  observer.  Since  the  true  vertex 
of  the  measured  angle  shifts  for  different  angles  the  sextant 
should  not  be  used  for  measuring  small  angles  between  ob- 
jects near  at  hand. 

ADJUSTMENTS.   Index   Glass,— To    make    the    index, 
glass,  I,  perpendicular  to  the  plane  of  the  -limb,  'bring  -the 
vernier  to  about  the  middle  of  the  arc  and  examine  the  arc 


132  TOPOGRAPHIC    SURVEYING. 

and  its  image  in  the  index  glass.  If  the  glass  is  perpendicu- 
lar to  'the  plane  of  the  limb,  the  image  of  the  reflected  and 
direct  portions  will  form  a  continuous  curve.  Adjust  the 
glass  by  means  of  the  screws  at  the  base. 

Horizon  Glass. — To  make  the  horizon  glass,  II,  parallel 
to  the  index  glass,  I,  for  a  zero  reading.  With  the  vernier 
set  to  read  zero,  sight  at  a  star  and  note  if  the  two  images 
are  in  exact  coincidence.  If  not,  adjust  the  horizon  glass 
until  they  are.  If  the  horizon  glass  cannot  be  adjusted, 
bring  the  images  into  coincidence  by  moving  the  arm  and 
read  the  vernier.  This  reading  is  the  index  error  which 
must  be  applied  with  its  proper  sign  to  all  the  angles 
measured. 

Line  of  Collimation.— To  make  the  line  of  collimation 
parallel  to  the  limb.  Place  the  sextant  on  a  plane  surface 
and  sight  at  a  point  about  20  feet  away.  Place  two  objects 
of  equal  height  on  the  extreme  ends  of  the  limb  and  note 
whether  both  lines  of  sight  are  parallel.  If  not,  adjust  the 
telescope  by  means  of  the  screws  in  "the  ring  that  carry  it. 

PROBLEMS  IN  TOPOGRAPHIC  SURVEYING. 

PROBLEM    El.      DETERMINATION    OF    STADIA    CON- 
STANTS OF  TRANSIT  WITH  FIXED  STADIA-HAIRS. 

(a)  Equipment. — Complete  transit,  stadia  rod.  steel  tape, 
set  chaining  pins,  foot  rule. 

(b)  Problem.— Det ermine  the  stadia  constants  c,  f  and  k 
for  an  assigned  transit. 

(c)  Methods. — (1)  Set  up  the  transit  and  set  ten  chaining 
pins  in  line  about  100  feet  apart  on  level  ground.    (2)  Plumb 
the  stadia  rod  by  the  side  of  the  first  pin.    (3)  Set  the  lower 
hair  on  an  even  foot  or  half  foot  mark  keeping  the  telescope 
nearly  level,  and  read  the  upper  stadia-hair.     (4)   Record 
the  intercept.     (5)  Read  the  intercept  on  the  rod  at  the  re- 
maining pins.     (6)  Measure  the  distance  from  the  center  of 
the  transit  to  each  pin  with  the  steel  tape.     (7)  Focus  the 
objective  on  a  distant  object,  measure  f  (the  distance  from 
the  plane  of  the  cross-hairs  to  the  center  of  the  objective), 
and  c(  the  distance  from  the  center  of  the  objective  to  the 
center  of  the  instrument).     (8)  Calculate  the  value  of  the 
stadia  ratio,   k,  for  each   distance  by  substituting   in   the 


PROBLEMS. 


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134  TOPOGRAPHIC   SURVEYING. 

fundamental  stadia  formula.  (9)  Take  the  arithmetical 
mean  of  the  ten  determinations  as  the  true  value.  (10)  Com- 
pute the  probable  error  of  a  single  observation  and  of  the 
mean  of  all  the  observations.  The  interval  factor  should 
be  determined  by  the  instrument  man  under  the  conditions 
of  actual  work.  The  determination  should  be  checked  at 
frequent  intervals  during  the  progress  of  the  field  work. 
Follow  the  prescribed  form. 

PROBLEM  E2.  STADIA  REDUCTION  TABLE. 

(a)  Equipment.— (No  instrumental  equipment  required.) 

(b)  Problem. — Compute  a  stadia  reduction  table  giving  the 
horizontal  distances  from  a  point  in  front  of  the  objective 
equal  to  the  principal  focal  distance  for  the  stadia  intervals 
from  0.01  feet  to  10  feet,  for  the  transit  used  in  Problem  El. 

(c)  Methods. — (1)  Prepare  form  for  calculation.     (2)  Com- 
pute the  horizontal  distances  by  substituting  the  different 
values  of  s  in  the  stadia  formula.    Compute  D'  for  values  of 
s  varying  from  0.01  foot  to  0.1  foot  varying  by  0.01  foot; 
from  0.1  foot  to  1  foot  varying  by  0.1  foot;  and  from  1  foot 
to  10  feet  varying  by  1  foot. 

(To  use  the  table,  take  the  sum  of  the  values  of  D'  cor- 
responding to  the  units,  tenths  and  hundredths  of  s  as  given 
in  the  table.  To  the  value  of  D'  thus  obtained  add  c  plus  f.) 

PROBLEM  E3.     AZIMUTH  TRAVERSE  WITH  TRANSIT 
AND  STADIA. 

(a)  Equipment. — Complete  transit,  stadia  rod,  steel  pocket 
tape. 

(b)  Problem. — Make  a  traverse  of  the  perimeter  of  an  as- 
signed field  with  a  transit  and  stadia. 

(c)  Methods. — (1)  Set  the  transit  over  one  corner  of  the. 
field  and  set  the  A  vernier  to  read  the  azimuth  of  the  pre- 
ceding course.     (2)  Sight  at  a  stadia  rod  held  edgewise  on 
the  last  station  to  the  left  with  the  telescope  normal  and 
clamp  the  lower  motion.    (3)  Read  the  intercept  on  the  rod 
to  the  nearest  0.01  foot.     (4)  Sight  at  the  target  set  at  the 
first  station  and  read  the  vertical  angle  to  the  nearest  min- 


PROBLEMS.  135 

ute.  (The  observer  should  measure  the  height  of  the  hori- 
zontal axis  above  the  station  with  the  steel  pocket  tape,  or 
one  tripod  leg  may  be  graduated  and  the  instrument  height 
determined  by  swinging  the  plumb  bob  out  against  the  leg.) 
(5)  Unclamp  the  upper  motion,  sight  at  the  next  station  to 
the  right  and  clamp  the  upper  motion.  (6)  Read  the  A  ver- 
nier, which  will  be  the  azimuth  of  the  course.  (7)  Read  the 
intercept  on  the  rod.  (8)  Measure  the  vertical  angle  by 
sighting  at  the  target  set  at  the  height  of  the  horizontal 
axis  as  before.  (9)  Set  the  transit  over  the  next  station  to 
the  right  and  determine  the  intercepts  and  vertical  angles  as 
at  the  first  station.  (10)  Determine  the  stadia  intercepts  and 
vertical  angles  at  the  remaining  stations,  passing  around  the 
field  to  the  right.  (11)  Reduce  the  intercepts  to  horizontal 
distances  before  recording.  (12)  Compute  the  vertical  dif- 
ferences in  elevation  using  mean  distances  and  vertical 
angles,  (13)  Compute  latitudes  and  departures  to  the  near- 
est foot  using  a  traverse  diagram  or  traverse  table.  Follow 
form  B4.  The  angular  error  of  closure  for  a  six-sided 
field  should  not  exceed  2'  Follow  the  prescribed  form  for 
the  field  notes. 

PROBLEM  E4.   SURVEY  OF  FIELD  WITH  PLANE 
TABLE  BY  RADIATION. 

(a)  Equipment — Plane  table,  stadia  rod,  2  flag  poles,  engin- 
eers' divided  scale,  drawing  paper,  6H  pencil. 

(b)  Problem— Make  a  survey  of  an  assigned  field  by  radi- 
ation with  the  plane  table. 

(c)  Met'hods. —  (1)  Set  the  plane  table  up  at  some  conven- 
ient point  in  the  field  and  select  a  point  on  the  drawing 
board  that  will  allow  the  entire  field  to  be  plotted  on  the 
paper.     (2)  Sight  at  one  of  the  stations  with  the  ruler  cen- 
tered on  the  point  on  the  paper.     (3)  Draw  a  line  along  the 
fiducial  edge  of  the  ruler  towards  the  point.     (4)  Measure 
the  distance  to  the  point  with  the  stadia.     (5)  Lay  off  the 
distance  on  the  paper  to  the  prescribed  scale.     (6)  Locate 
the  remaining  points  in  the  same  manner.     (7)   Complete 
the  map  in  pencil.    The  map  should  have  a  neat  title,  scale, 
meridian,  etc.     (8)   Trace  the  map  on   tracing  linen.     (9) 
Compute  the  area  by  the  perpendicular  method,  scaling  the 
dimensions  from  the  map. 


136  TOPOGRAPHIC  SURVEYING. 

PROBLEM  E5.     SURVEY   OF  A   FIELD    WITH     PLANE 
TABLE   BY  TRAVERSING. 

(a)  Equipment— Plane  table,  stadia  rod,  2  flag  poles,  engin- 
eers' divided  scale,  drawing  paper,  6H  pencil. 

(b)  Problem. — Make  a  survey  of  an  assigned  field  by  tra- 
versing with  the  plane  table. 

(c)  Methods: — Follow  the  same  general  methods  as  those 
given  for  traversing  with   the  transit.     Adjust   the   plane 
table  before  beginning  the  problem.    Complete  the  map  and 
compute  the  area  as  in  Problem  E4. 

PROBLEM  E6.   SURVEY  OF  FIELD  WV^H  PLANE 
TABLE  BY  INTERSECTION. 

(a)  Equipment.— Plane  table,  2  flag  poles,  engineers   divid- 
ed scale,  drawing  paper,  6H  pencil. 

(b)  Problem. — Make  a  survey  of  an  assigned  field  with  tfc.3 
plane  table  by  intersection. 

(c)  Methods. —  (1)  Select  and  measure  -a  base  line  having 
both  ends  visible  from  all  the  stations  in  the  field.     (2)  Set 
the  plane  'table  over  one  end  of  the  base  line  and  sight  at 
the  other  end   of  the  base  line  and  at  each   one   of   the 
stations  of  the  field.     (3)  Set  the  plane  table  over  the  other 
end  of  the  base  line,  orient  the  instrument  by  sighting  at 
the  station  first  occupied  and  sight  at  all  the  stations  in  the 
field.     (4)  Complete  the  map  and  compute  the  area  as  in 
Problem  E4. 

PROBLEM  E7.    THREE  POINT  PROBLEM  WITH  PLANE 
TABLE. 

(a)  Equipment— Plane  table,  2  flag  poles,  engineers'  divid- 
ed scale,  6H  pencil. 

(b)  Problem. — Having  three  points  plotted  on  the  map,  re- 
quired to  locate  a  fourth  point  on  the  map  by  solving  the 
"three  point  problem"  with  the  plane  table. 

(c)  Methods. — (1)   Use  Bessell's  solution.     (2)   Check  by 
using  the  mechanical  solution. 

PROBLEM    E8.     ANGLES    OF    TRIANGLE   WITH   SEX- 
TANT. 

(a)  Equipment. — Sextant,  2  flag  poles. 


PROBLEMS.  137 

(b)  Problem. — Measure  the  angles  of  an  assigned  triangle 
with  the  sextant. 

(c)  Method*.— -(I)  Set  the  flag  poles  behind  the  monuments 
at  two  of  the  vertices  of  the  triangle  and  stand   on   the 
monument  at  the  third.     (2)  Hold  the  plane  of  the  sextant 
horizontal,   sight  at  one  flag  pole  directly  with   the   tele- 
scope and  bring  the  image  of  the  other  flag  pole  into  coin- 
cidence by  moving  the  arm.     (3)   Read  the  vernier.     This 
reading  is  the  angle  sought.     (4)  Repeat  the  measurement 
with  the  sextant  inverted.    Take  the  mean  of  the  two  read- 
ings, which  should  not  differ  more  than  2'  as  the  true  value 
of  the  angle.     (5)   Measure  the  other  angles  in  the  same 
manner.    The  error  of  closure  should  not  exceed  3'.  Record 
the  data  in  a  suitable  form. 

PROBLEM    E9.      DETERMINATION    OF   COEFFICIENTS 
OF  A  TAPE. 

(a)  Equipment.— Steel  tape,  spring  balance,  2  thermom- 
eters, steel  rule,  2  stout  stakes,  axe,  2  pieces  sheet  zinc  2  by 
2  inches. 

(b)  Problem.— Determine  the  coefficients    of    expansion, 
stretch  and  sag  for  an  assigned  tape.     Make  three  deter- 
minations of  each  and  take  the  arithmetrical  mean  as  the 
true  value. 

(Standard  Tape*. — In  laying  off  a  standard  or  measuring 
a  base  line  where  a  high  degree  of  precision  is  required  it 
is  important  that  all  measurements  be  referred  to  the  same 
standard1.  The  Bureau  of  Weights  and  Measures  of  the  U. 
S.  Coast  and  Geodetic  Survey,  Washington,  D.  C.,  will  com- 
pare a  tape  with  the  government  standard  for  a  small  fee. 
The  tape  tested  is  certified  to  be  of  a  given  length  for  a 
given  temperature  and  pull.  For  example  the  standard  tape 
marked  "U.  S.  W.  &  M.  215"  used  in  laying  off  the  100-ft. 
standard  in  Problem  A.  23,  was  certified  to  be  99.9967  feet 
long  at  a  temperature  of  62°  F.  and  a  pull  of  12  pounds  when 
tested  on  a  plane  surface.  The  coefficient  of  expansion  of 
this  tape  was  0.0000061  per  degree  F.) 

(c)  Methods. — (1)   Correction  for  Expansion. — Measure  the 
length  of  the  tape  on  a  plane  surface  at  two  different  tem- 
peratures but  with  a  constant  pull  determined  by  a  spring 
balance.     Then  substitute  the  lengths,  1  and  L,  and  tem- 
peratures, t  and  T  in  the  formula 


138  TOPOGRAP1HC  SURVEYING. 

1  —  L  =  e  (  t  —  T  )  1 

where  e  is  the  coefficient  of  expansion.  Repeat  the  test 
and  obtain  three  values  of  the  coefficient  e.  As  large  a 
range  of  temperatures  as  possible  should  be  secured.  Take 
the  arithmetrical  mean  of  the  three  determinations  as  the 
true  value. 

(2)  Correction  for  Stretch. — Measure  the  length  of  the  tape 
on  a  plane  surface  with  two  different  pulls  but  at  a  constant 
temperature.     Determine  the  pull  with  a  spring  balance. 
Then  substitute  the  lengths  1  and  L  and  the  pu,lls  p  and  P 
in  the  formula 

1  —  L  =  s  (  p  —  P  )  1 

where  s  is  the  coefficient  of  stretch.  Repeat  the  test  and 
obtain  three  values  of  the  coefficient  s.  The  pulls  should 
range  from  10  to  40  pounds.  Take  the  arithmetical  mean 
of  the  three  determinations  as  the  true  value. 

(3)  Correction  for  Sag. — Remove  the  handles  from  the  taps 
and  determine  its  weight  very  carefully.    Divide  the  weight 
by  the  length  to  obtain  the  weight  per  foot,  w.     Drive  two 
stout  hubs  a  little  less  than  100  feet  apart  and  fasten  a  piece 
of  sheet  zinc  with  a  line  ruled  at  right  angles  to  the  line  on 
the  top  of  each  stake.    With  a  pull  of  10  pounds,  as  deter- 
mined by  the  spring  balance,  measure  the  distance  between 
the  stakes.    Calculate  the  correction  for  sag  by  substituting 
the  lengths  1  and  L,  pull  p,  and  weight  per  foot  w,  in  the 
formula. 

1-L=214  (y)2 

Repeat  the  measurements  using  a  pull  of  20  and  30  pounds, 
respectively.  Add  the  corrections  for  sag  to  each  measure- 
ment and  compare  the  results.  The  temperature  should  re- 
main constant  during  the  tests.  To  remove  the  possibility 
of  an  error  due  to  temperature,  observe  the  temperature  at 
the  time  of  each  observation  and  correct  the  observed 
length  for  expansion  before  substituting  in  the  formula. 

Report  the  methods,  data,  computations  and  results  on  a 
suitable  form. 

(a)   Equipment. — Standard  tape,  transit  or  level,    stakes 


PROBLEMS.  139 

PROBLEM  E10.     MEASUREMENT  OP  BASE  LINE. 

i 

(number  and  size  to  be  specified  by  instructor),  axe,  spring 
balance,  2  thermometers,  lath  stakes,  8-d  nails,  steel  rule, 
pieces  sheet  zinc  2  by  2  inches. 

(b)  Problem. — Measure  an  assigned  base  line  with  a  stan- 
dard tape.    Support  the  tape  at  intervals  of  20  feet  and  note 
the  pull  and  temperature.     Make  at  least  three  determin- 
ations of  the  length  of  the  base  line.    Reduce  the  observed 
results  to  the  standard  by  making  corrections  for  standard, 
expansion,  sag,  stretch  and  slope.     Take  the  arithmetical 
mean  of  all  the  determinations  as  the  true  value. 

(c)  Methods. — (1)  Set  the  transit  over  one  end  of  the  base 
line,  sight  at  the  other  end  and  determine  the  difference 
in  elevation  and  grade.     (2)   Drive  stout  square  stakes  to 
grade  by  "shooting"  them  in  with  the  instrument  in  true 
line    a    little    less    than    a    full    tiape    length    apart.     The 
tops  of  the  lowest  stake  should  not  be  less  than  6  inches 
above  the  ground.     (3)  Fasten  a  piece  of  sheet  zinc  with  a 
fine  line  ruled  at  right  angles  to  the  direction  of  the  base 
line  on  the  top  of  each  stake.     (4)  Drive  lath  stakes  in  line 
about    20    feet    apart.     (5)      Drive    an    8-d    nail    through 
each  lath  stake  at  grade  to  support  the  tape.     (6)  Measure 
from  stake  to  stake,  the  men  working  as  follows:     No.  1 
plumbs  up  from  the  rear  monument  or  holds  the  zero  on 
the  mark  on  the  rear  stake;  No.  2  takes  the  spring  balance 
and  puts  a  pull  of  16  pounds  on  the  tape;  No.  3  reads  the 
tape  and  measures   the  fraction   of  a  tenth   with   a  steel 
rule  to  0.001  feet;  No.  4  records  the  reading  of  the  tape  and 
reads  the  two  thermometers  placed  at  the  quarter  points 
of  the  tape.    (7)  Obtain  at  least  three  determinations  of  the 
length  of  the  base  line.     (8)  Correct  each  measurement  of 
the  base  for  standard,  expansion,  sag,  stretch,   and  slope 
(see  problem  on  coefficients  of  a  tape).    The  three  measure- 
ments  should    not    differ    more    than     1:100,000.      Report 
methods,  computations  and  results  on  a  suitable  form. 

PROBLEM   Ell.      CALCULATION   OF   TRIANGULATION 
SYSTEM. 

(a)  Equipment — Seven-place  table  of  logarithms. 

(b)  Problem.— Adjust  and  calculate  an  assigned  triangula- 
tion  system  and  plot  the  skeleton. 


140  TOPOGRAPHIC  SURVEYING. 

(c)  Methods. — Observe  the  following  program:  (1) 
prepare  forms  for  calculation  and  transcribe  data;  (2)  ad- 
just the  angles  of  the  triangulation  system  (see  chapter  on 
errors  of  surveying) ;  (3)  calculate  the  front  and  back  azi- 
muths of  each  line;  (4)  beginning  with  the  base  line  com- 
pute the  sides,  to  the  nearest  0.001  foot;  (5)  calculate  the 
latitudes  and  departures  to  the  nearest  0.001  foot.  (6)  cal- 
culate the  coordinates  of  the  triangulation  stations  to  the 
nearest  0.001  foot.  In  computing  the  coordinates  of  the 
stations  take  the  mean  of  the  values  found  by  taking  the 
different  routes  from  the  base  line  as  the  true  value.  (7) 
Plot  the  skeleton  of  the  triangulation  system  to  the  pre- 
scribed scale  by  means  of  the  coordinates  of  the  points. 
The  plotting  sheet  should  be  ruled  off  into  squares  very 
carefully  before  beginning  the  plotting.  For  this  purpose 
use  a  steel  straight  edge  and  beam  compass. 

PROBLEM  E12.     SKETCHING  TOPOGRAPHY. 

(a)  Equipment. — Small  drawing  board  or  plane  table,  plat 
of  assigned  field,  4H  pencil. 

(b)  Problem. — Sketch  in  the  roads,  walks,  buildings  and 
five  foot  contours  on  the  plat  of  the  assigned  field  by  eye 
having  given  the  elevations  of  the  ruling  points. 

(c)  Methods—  (1)  Transfer  from  the  level  notes  to  the  plat 
the  elevations  of  the  ruling  points  of  the  field.     (2)  Locate 
the  roads,  buildings,  etc.,  on  the  map  as  nearly  as  possible 
in  their  relative  positions   (the  topographers'  estimate  of 
distances  should  be  frequently  checked   by   pacing.)      (3) 
Estimate  the  slopes  and  locate  the  contour  points  between 
the  points  of  known  elevation.     (4)   Join  these  points  by 
smooth  curved  lines.     (5)  Finish  the  map  in  pencil,  putting 
on  a  neat  title,  the  scale  of  the  map  and  a  meridian.     (6) 
Compare  the  finished  map  with  a  contour  map  furnished  by 
the  instructor. 

PROBLEM  E13.     FILLING  IN  DETAILS  WITH  TRANSIT 
AND  STADIA. 

(a)  Equipment. — Complete  transit,   2   stadia  rods,   pocket 
tape. 

(b)  Problem.— Locate  the  topographic    details    of   an    as- 
signed area  with  the  transit  and  stadia. 


PROBLEMS. 


141 


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(c)  Methods — (1)  Set  the  transit  over  one  corner  of  the 
field  and  set  the  A  vernier  to  read  the  azimuth  of  a  triangu- 
lation  line.  (2)  Sight  at  the  s'tadia  rod  held  sidewise  on  the 
triangulation  station  at  the  other  end  of  the  given  line,  with 
the  telescope  normal  and  clamp  the  lower  motion.  (3) 
Read  the  intercept  on  the  rod  to  the  nearest  0.01  foot.  Re- 
duce this  reading  and  check  the  ratio  k  by  comparing  the 
observed  with  the  known  distance.  (4)  Sight  at  target  of 
the  stadia  rod  or  a  rubber  band  at  the  height  of  the  hori- 
zontal axis  of  the  instrument  above  the  first  station  and 
read  the  vertical  angle  to  the  nearest  minute.  (5)  Unclamp 
the  upper  motion  and  take  side  shots  to  locate  the  topo- 
graphic details.  In  taking  the  side  shots  read  the  intercept 
first,  then  set  the  middle  cross-hair  on  the  target  and  signal 
the  rod  man  all  right.  The  vertical  angle  and  azimuth 
can  then  be  read.  Enough  side  shots  should  be  taken  to  lo- 
cate representative  points,  ridges,  gullies,  etc.,  on  the  sur- 
face that  can  be  shown  on  the  finished  map.  The  scale  of 
the  map  should  therefore  be  known  before  beginning  the 
field  work.  It  is  usually  best  to  run  along  the  top  of  a  ridge 
and  take  side  shots  on  both  sides.  (6)  After  all  the  side 
shots  have  been  taken  at  the  first  triangnlqtion  station 


142  TOPOGRAPHIC  SURVEYING. 

select  a  stadia  station  at  a  convenient  point.  (7)  Sight  at 
the  edge  of  the  stadia  rod  held  on  the  stadia  station  and 
clamp  the  upper  motion.  (8)  Read  the  A  vernier  which 
will  be  the  azimuth  of  the  course.  (9)  Read  the  intercept 
on  the  rod.  (10)  Measure  the  vertical  angle  as  before.  Set 
the  transit  over  the  stadia  station  and  orient  as  at  the  first 
station.  Take  side  shots  as  at  the  first  station.  Continue 
around  the  field,  connecting  the  stadia  stations  by  a  closed 
traverse  as  in  Problem  E3.  Record  the  field  notes  in  the 
prescribed  form.  (11)  Reduce  the  field  notes  by  using  either 
the  slide  rule,  tables,  or  diagrams,  and  check  in  part  by 
using  one  of  the  remaining  methods.  (12)  Plot  the  stadia 
traverse  and  sid<e  shots  using  a  protractor.  Number  each 
point  plotted  on  the  map  and  write  its  elevation  just  below 
the  number  in  the  form  of  a  fraction.  (13)  Locate  the  con- 
tours by  interpolating  between  the  plotted  points  and  com- 
plete the  map  in  pencil  on  manila  paper.  (14)  Trace  the 
map  if  required. 

PROBLEM   E14.     FILLING   IN   DETAILS  WITH   PLANE 
TABLE  AND  STADIA. 

(a)  Equipment. — Complete  plane  table    (preferably    with 
prismatic  eyepiece),  2  stadia  rods,  engineers'  divided  scale, 
drawing  paper,  6H  pencil,  pocket  tape. 

(b)  Problem. — Locate  the  topographic  details    of    an    as- 
signed area  with  the  plane  table  and  stadia. 

(c)  Methods — Follow  the  same  methods  as  in  Problem  E13 
except  that  the  notes  are  to  be  plotted  on  the  drawing  paper 
in  place  of  being  recorded  in  the  field  book.    Mark  the  point 
by  number  and  write  the  elevation  of  each  point  under  the 
number  in  the  form  of  a  fraction.    Locate  the  contour  points 
by  interpolation  on  the  map   and  connect  the  points  by 
smooth  curves.     Complete  the  map  in  pencil  and  make  a 
tracing  if  required. 

PROBLEM  E15.  TOPOGRAPHIC  SURVEY. 

(a)  Equipment. — Complete  transit,  2  stadia  rods,  stakes, 
hubs,  spring  balance,  pocket  tape,  stadia  slide  rule,  seven- 
place  logarithm  table,  (extra  tripods,  stadia  reduction  table 
stadia  reduction  diagrams,  etc.,  as  required). 


PROBLEMS.  143 

(b)  Problem. — Make  a  Complete  topographic  survey  of  an 
assigned  area  and  make  a  topographic  map. 

(c)  Methods — (1)   Make  a  reconnaissance  and  locate  the 
triangulation  stations.     Care  should  be  used  to  select  the 
triangulation  stations  so  that  the  sights  will  be  clear  and 
the  triangles  well  formed.     A  system  composed  of  quad- 
rilaterals or  more  complicated  figures  will  give  more  con- 
ditions and  checks  than  a  simple  string  of  triangles.     A 
system  composed  of  simple  triangles  is  sufficient  for  this 
survey.     (2)  Mark  the  triangulation  stations  with  gas  pipe 
monuments  about  4  feet  long,  the  exact  point  being  marked 
by  a  hole  drilled  in  a  bolt  .screwed  into  a  cap  on  the  top  of 
the  gas  pipe.     (3)  Measure  the  base  line  and  base  of  veri- 
fication  as   described    in    Problem    E10.      (4)    Measure   the 
angles  by  repetition  as  depcribed  in  Problem  DIG.  (5)  Cal- 
culate the  skeleton  as  described  in  Problem  Ell.     (6)  Estab- 
lish permanent  bench  marks  and  determine  their  elevations 
and  the  elevation  of  the  stations  of  the  triangulation  sys- 
tem by  running  duplicate  levels  with  the  engineers'  level 
reading  the  rod  *o  0.001  foot.     (7)  Fill  in  the  details  with 
either  the  transit  and  stadia  or  the  plane  table  and  stadia, 
or  both,  as  described  in  Problems  E13  and  E14.     (8)  Com- 
plete the  map  in  pencil  on  manila  paper,  and  after- it  has 
been  approved  by  the  instructor  trace  it  on  tracing  linen. 
The  title,  meridian,  scale,  lettering  and  border  should  re- 
ceive careful  attention. 


PROBLEM  E16.     LEVELS  FOR  PROFILE  AND  QUANTI- 
TIES FOR  PAVING  A  STREET. 

(a)  Equipment. — Level,  level  rod,  4  flag  poles.  100-foot  steel 
tape,  chaining  pfns,  50-foot  metallic  tape,  hubs,  axe. 

(b)  Problem. — Take  level  rod  readings  on  the  center  line, 
right  and  left  curb  lines,  right  and  left  sidewalk  lines,  and 
right  and  left  property  lines  to  determine  profiles  and  quan- 
tities for  paving1  street.     Plot  profiles  on  Plate   A  profile 
paper  to  a  scale  of  40  feet  to  1  inch  horizontal  and  4  feet  to 
1  inch  vertical.    Estimate  the  quantities  of  cut  and  fill  and 
paving  materials. 

(c)  Vetfi od. *— (1)  Locate  the  center  line  of  the  street  and 
set  flag  poles  on  line  about  400  feet  apart  by  ranging  in 
with  the  eye.  (2)  Drive  a  hub  at  one  end  of  the  street  and  call 


144 


TOPOGRAPHIC  SURVEYING. 


this  point  station  zero.  (3)  Run  a  line  of  differential  levels 
from  the  Standard  B.  M.  to  the  zero  end  of  the  line.  Read 
the  rod  to  0.01  fort.  (4)  Read  the  level  rod  to  0.1  foot  on  the 
ground  at  center  hub.  (5)  Measure  the  distance  out  to  the 
right  curb  line,  right  sidewalk  and  right  property  lines 
with  the  metallic  tape  and  read  the  rod  to  0.1  foot  on  the 
ground.  (6)  Repeat  for  the  left  side.  (7)  Chain  along  the 
center  line  to  station  1.  (8)  Measure  to  the  right  and  left 
from  the  chaining  pin  the  required  distances  with  the 
metallic  tape  and  take  rod  readings  as  at  station  zero.  (9) 
Repeat  the  process  at  each  station  and  at  abrupt  changes 
intermediate.  (10)  Check  the  level  circuit.  (11)  Make  pro- 
file on  Plate  A  paper,  scales  40  feet  to  the  inch  horizontal 
and  4  feet  vertical,  indicating  the  several  lines  by  conven- 
tional lines  or  cclors.  (12)  Lay  grade  line  as  directed.  (13) 
Show  plat  at  bottom  of  profile.  (14)  Plot  sections  at  scale 
of  20  feet  to  the  inch  and  determine  areas.  (15)  Compute 
quantities  of  earthwork,  paving,  etc.  Follow  form. 


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CHAPTER  VII. 
LAND  SURVEYING. 


Kinds  of  Surveys. — Surveys  of  land  are  of  two  kinds: 
(a)  original  surveys;  (b)  resurveys. 

Original  Surveys. — An  original  survey  is  made  for  the 
purpose  of  establishing  monuments,  corners,  lines,  bound- 
aries, dividing  land,  etc.  The  survey  of  a  townsite  and  the 
government  survey  of  a  section  are  examples  of  original 
surveys. 

Resurveys.— A  resurvey  is  made  for  the  purpose  of  iden- 
tifying and  locating  corners,  monuments,  lines  and  bound- 
aries that  have  been  previously  established.  The  resurvey  of 
a  city  block,  or  a  survey  to  relocate  a  section  corner  are 
examples  of  resurveys. 

Functions  of  a  Surveyor. — In  an  original  survey  it  is 
the  function  of  the  surveyor  to  make  a  perfect  survey,  es- 
tablish permanent  monuments  and  true  markings,  and  make 
a  correct  record  of  his  work  in  the  form  of  field  notes  and 
a  plat. 

In  a  resurvey  it  is  the  function  of  the  surveyor  to  find 
where  the  monuments,  courses,  lines  and  boundaries  orig- 
inally were,  and  not  where  they  ought  to  have  been.  Fail- 
ing in  this  it  is  his  business  to  reestablish  them  as  nearly  as 
possible  in  the  same  place  they  were.  No  reestablished 
monument,  no  matter  how  carefully  relocated  will  have  the 
same  weight  as  the  original  monument  if  the  latter  can  be 
found.  In  making  resurveys  the  surveyor  has  no  official 
power  to  decide  disputed  points.  He  can  only  act  as  an 
expert  witness.  If  the  interested  parties  do  not  agree  to 
accept  his  decision  the  question  must  be  settled  in  the 
courts. 

Rules  for  Resurveys. — The  following  rules  may  be  safe- 
ly observed  in  making  resurveys. 

(1)  The  descriptions  of  boundaries  in  a  deed  are  to  be 
taken  as  most  strongly  against  the  grantor. 

(2)  A  deed  is  to  be  construed  so  as  to  make  it  effectual 
rather  than  void. 

(3)  The  certain  parts  of  a  description  are  to  prevail  over 
the  uncertain. 


146  LAND  SURVEYING. 

(4)  A  conveyance  by  metes  and  bounds  will  convey  all 
the  land  included  within. 

(5)  Monuments   determine   boundaries   and   transfer   all 
the  land  included. 

(6)  When  a  survey  and  a  map  disagree  the  survey  pre- 
vails. 

(7)  Marked  lines  and  courses  control  courses  and   dis- 
tances. 

(8)  The  usual  order  of  calls   in  a   deed  is:     natural  ob- 
jects, artificial  objects,  course,  distance,  quantity. 

(9)  A  long  established  fence  line  is  better  evidence  of 
actual  boundaries  than  any  survey  made  after  the  monu- 
ments of  the  original  survey  have  disappeared. 

(10)  A  resurvey  made  after  the  monuments  have  disap- 
peared is  to  determine  where  they  were  and  not  where  they 
ought  to  have  been. 

(11)  All  distances  measured  between  known  monuments 
are  to  be  pro  rata  or  proportional  distances. 

If  the  above  rules  do  not  cover  the  case  in  question  spe- 
cial court  decisions  on  that  particular  point  should  be  con- 
sulted. 

THE    UNITED   STATES    RECTANGULAR     SYSTEM     OF 
PUBLIC  LAND  SURVEYS. 

Historical.— The  United  States  rectangular  system  of 
subdividing  lands  was  adopted  by  congress  May  20,  1785. 
The  first  public  land  surveys  were  made  in  the  eastern  part 
of  the  present  state  of  Ohio  under  the  direction  of  Capt. 
Thomas  Hutchins,*  Geographer  of  the  United  States,  and 
were  known  as  the  "Seven  Ranges".  The  tov/r: ships  were 
six  miles  square,  and  were  laid  out  in  ranges  extending 
northward  from  the  Ohio  river;  the  townships  were  num- 
bered from  south  to  north,  the  ranges  from  east  to  west. 
In  these  initial  surveys  only  the  exterior  lines  of  the  town- 

*The  earliest  published  reference  to  the  rectangular  sys- 
tem of  land  surveys  is  found  in  an  appendix  to  "Bouquet's 
Mardh,"  published  in  Philadelphia,  1764.  Hutchins  was 
engineer  with  this  expedition  to  the  forks  of  the  Muskingum 
river,  and  wrote  the  appendix.  (See  reprint  by  Robt. 
Clarke,  Cincinnati.) 


UNITED  STATES  LAND  SURVEYS.  147 

were  run,  but  mile  corners  were  established  on  the 
township  lines,  and  sections  one  mile  square  were  marked 
on  the  plat  and  numbered  from  1  to  36,  commencing  with 
section  1  in  the  southeast  corner  and  running  from 
south  to  north  in  each  tier  to  36  in  the  northwest  section. 

The  act  of  congress  approved  May  18,  1796,  provided  for 
the  appointment  of  a  surveyor  general  and  changed  the  law 
relating  to  the  surveys  of  public  lands.  Under  this  law  the 
townships  were  subdivided  into  sections  by  running  paral- 
lel lines  two  miles  apart  each  v/ay  and  setting  a  corner  at 
the  end  of  each  mile.  This  law  also  provided  that  the  sec- 
tions be  numbered  beginning  with  section  1  in  the  north- 
east corner  of  'the  (township,  thence  west  and  east  alter- 
nately to  36  in  the  southeast  section.  This  is  the  method 
of  numbering  still  in  use,  shown  in  Figs.  33  and  34. 

The  act  of  congress  approved  May  10,  1800,  required  that 
townships  be  subdivided  by  running  parallel  lines  through 
the  same  from  east  to  west  and  from  south  to  north  at  a 
distance  of  one  mile  from  each  other.  Section  corners  and 
half  section  corners  on  the  lines  running  from  east  to  west 
were  required  to  be  set.  The  excess  or  deficiency  was  to  be 
thrown  into  the  north  and  west  tiers  of  sections  in  the 
townships. 

The  act  of  congress  approved  February  11,  1805,  required 
that  interior  section  lines  be  run  every  mile;  that  corners 
be  established  every  half  mile  on  both  townships  and  sec- 
tion lines;  that  discrepancies  be  thrown  on  the  north  and 
west  sides  of  the  township.  This  act  of  congress  further 
provided  "that  all  corners  marked  in  the  original  surveys 
shall  be  established  as  the  proper  corners  of  sections,  or 
subdivisions  of  sections;  and  that  corners  of  half  and 
quarter  sections  not  marked  shall  be  placed  as  nearly  as 
possible  "equidistant"  from  those  two  corners  which  stand 
on  the  same  line.  The  boundary  lines  actually  run  and 
marked  shall  be  established  as  the  proper  boundary  lines 
of  the  sections  or  subdivisions  for  which  they  were  intend- 
ed; and  the  length  of  such  lines  as  returned  by  the  surveyor 
shall  be  held  and  considered  as  the  true  length  thereof,  and 
the  boundary  lines  which  shall  not  have  been  actually  run 
and  marked  as  aforesaid  shall  be  ascertained  by  running 
straight  lines  from  the  established  corners  to  the  opposite 
corresponding  corners."  Under  this  law,  which  is  still  the 


148 


LAND  SURVEYING. 


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established  rule  of  procedure,  each  reported  distance  be- 
tween established  monuments  is  an  independent  unit  of 
measure. 

The  revised  instructions  issued  in  1855  required  that  the 
sections  be  subdivided  as  shown  in  Fig.  33,  the  full  lines, 
representing  "true"  lines,  are  parallel  to  the  east  exterior 
line  of  the  township,  and  the  dotted  lines,  representing 
"random"  lines,  close  on  corners  previously  established. 
The  order  of  the  survey  of  the  interior  section  lines  is  in- 
dicated by  the  small  numerals.  Double  corners  on  the 
north  and  west  township  lines,  which  were  common  in  the 
earlier  surveys,  were  thus  avoided  in  the  revised  practice. 

Laws  Inconsistent. — It  is  obviously  impossible  to  pre- 
serve a  true  rectangular  system  on  a  spherical  surface,  ow- 


UNITED   STATES   LAND   SURVEYS.  149 

ing  to  the  convergency  of  meridians.*  To  harmonize  the 
methods  of  making  surveys,  the  General  Land  Office  has 
issued  instructions  for  the  survey  of  public  lands  from  time 
to  time. 

DETAILS  OF  SURVEY.— The  details  of  the  survey  are 
taken  up  in  the  following  order:  (1)  selection  of  initial 
points;  (2)  establishment  of  the  base  line;  (3)  establish- 
ment of  the  principal  meridian;  (4)  running  standard  paral- 
lels; (5)  running  the  guide  meridians;  (6)  running  the 
township  exteriors;  (7)  sirbdividing  the  township;  (8) 
meandering  lakes,  rivers,  streams,  etc.  See  Figs.  32  and  33. 

Initial  Points. — Initial  points  from  which  to  start  the 
survey  are  established  whenever  necessary  iinder  special 
instructions  prescribed  by  the  Commissioner  of  the  General 
Land  Office. 

Base  Line. — The  base  line  is  extended  east  and  west 
from  the  initial  point  on  a  parallel  of  latitude.  The  proper 
township,  section  and  quarter  corners  are  established  and 
meander  corners  at  the  intersection  of  the  line  with  all 
meanderable  streams,  lakes,  or  bayous.  Two  sets  of  chain- 
men  are  employed  and  the  mean  of  the  two  measurements 
is  taken  as  the  true  value.  When  the  transit  is  used,  the 
base  line — which  is  a  small  circle  parallel  to  the  equator — 
is  run  by  making  offsets  from  a  tangent  or  secant  line,  the 
direction  of  the  line  being  frequently  checked  by  an  observ- 
ation of  Polaris. 

Principal  Meridian. — The  principal  meridian  is  extend- 
ed either  north  or  south,  or  in  both  directions  from  the 
initial  point  on  a  true  meridian.  The  same  precautions  are 
observed  as  in  the  measurement  of  the  base  line. 

Standard  Parallels. — Standard  parallels,  which  are  also 
called  correction  lines,  are  extended  east  and  west  from  the 
principal  meridian,  at  intervals  of  24  miles  north  and 
south  of  the  base  line.  They  are  surveyed  like  the  base  line. 

Guide  Meridians. — Guide  meridians  are  extended  north 


*The  angular  convergency,  a,  of  two  meridians  is  m  sin  L, 
where  m  is  the  angular  difference  of  longitude  of  meridians 
and  L  is  the  mean  latitude  of  the  two  positions.  The  linear 
convergency,  c,  for  a  length,  t,  is  t  sin  a.  For  latitude  40°, 
the  difference  between  the  north  and  south  sides  of  a  town- 
ship is  0.60  chains. 


150 


LAND  SURVEYING. 


t 
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36 

Fig.  33. 


from  the  base  line,  and  standard  parallels,  at  intervals  of 
24  miles  east  and  west  from  the  principal  meridian,  in  the 
manner  prescribed  for  running  the  principal  meridian. 
When  existing  conditions  require  that  guide  meridians  shall 
be  run  south  from  the  base  or  correction  lines,  they  are 
initiated  at  properly  established  closing  corners  on  such 
lines. 

Township  Exteriors.— The  township  exteriors  in  a  tract 
24  miles  square,  bounded  by  standard  lines,  are  surveyed 
successively  through  the  block,  beginning  with  the  south-- 
western township.  The  meridional  boundaries  are  run  first 
form  south  to  north  on  true  meridians  with  permanent  cor- 
ners at  lawful  distances;  the  latitudinal  boundaries  are  run 
from  east  to  west  on  random  or  trial  lines  and  corrected 


UNITED  STATES   LAND  SURVEYS. 


151 


First  t'ian^a    I'    Parallel    \     North        I T 

.f"   I       Sec.k        I      sZc.S*  ^c!^       I      Sec.  1        ' 


aftow  ;>ta  ivprwnfc  a  theoretical  township  with  perfect  tvbdMtion*, 
cmttyiu>u»  to  the  north  side  of  a  Standard  Parallel;  in  assumed  Latitude 
42  15' N..  and  Longitude  100°00'  W.  of  Cr.  Area  M024.J6  A, 

Fig.  34. 

back   on   true   lines.     Allowance   for   the   convergency   of 
meridians  is  made  whenever  necessary. 

Township  Subdivision. — A  true  meridian  is  established 
at  the  southeast  corner  of  the  township  and  the  east  and 
south  boundaries  of  section  36  are  retraced.  Then  begin- 
ning at  the  corner  to  sections  35  and  36  on  the  southern 
boundary,  a  line  is  run  north  parallel  to  the  range  line, 
corners  are  established  at  a  distance  of  40  and  80  chains; 
from  the  last  named  corner  a  random  line  is  run  eastward, 
parallel  to  the  south  boundary  line  of  section  36,  to  its 
intersection  with  the  east  boundary  of  the  township.  A 
temporary  corner  is  set  at  a  distance  of  40  chains,  and  a 
permanent  corner  is  afterwards  established  midway  be- 


52 

LAND 

39.94 

0 

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o 

8 

1                      6 

j        39.82 

I 

|        39.8£ 

(G) 


Fig.  35. 


tween  the  two  permanent  corners.  The  other  corners  are 
located  in  a  similar  manner,  as  shown  in  Pig.  33.  The  lines 
closing  on  the  north  and  west  boundary  lines  of  the  town- 
Ship  are  made  to  close  on  the  section  corners  already  es- 
tablished. A  theoretical  township  with  perfect  subdivisions 
is  shown  in  Fig.  34. 

Meandering.— Navigable  rivers  and  other  streams  hav- 
ing a  width  of  three  chains  and  upwards  are  meandered  on 
both  banks,  at  the  ordinary  hig'h  water  line  by  taking  the 
general  courses  and  distances  of  their  sinuosities.  The 
meanders  of  all  lakes,  navigable  bayous,  and  deep  ponds  of 
the  area  of  twenty-five  acres  and  upwards  are  surveyed  as 


UNITED  STATES  LAND  SURVEYS. 


153 


11 

«**»** 

10  Ac. 

40  A<-               nE.% 

i:, 

w  2                                  I6O  Ac. 

640    Ac. 

w.i 

E-~L                     5£  - 

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s.w.~ 

dO  Ai,.                    160  Ac. 

\ 

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Fig.  36. 

directed  for  navigable  streams.  Meander  corners  are  estab- 
lished where  meander  lines  cross  base  lines,  township  lines, 
or  section  lines. 

Subdivision  of  Sections.— In  Fig.  35,  (a)  gives  the  sub- 
division of  an  interior  section,  (b)  of  section  2  on  the  north 
side,  (c)  of  section  7  in  the  west  tier,  and  (d)  of  section  6 
in  the  northwest  corner. 

Description  of  Land.— Land  is  described  in  the  rectan- 
gular system  by  giving  its  Location  in  a  civil  township;  for 
example,  in  Fig.  36,  the  northwest  quarter,  containing 
160  acres,  would  be  described  as:  N  E  14,  Sec.  8,  T  19  N, 
R  9  E,  3  P.  M.  The  ten  acre  lot  indicated  in  tlhe  northwest 
quarter  would  be  described  as:  S  E  y±,  N  W  %,  N  W  *4, 
Sete.  8,  T  19  N,  R  9  E,  3  P.  M. 

Corners. — The  corner  monuments  may  be  as  follows: 
(a)  stone  with  pits  and.  earthen  mound;  (b)  stone  with 
mound  of  stone;  (c)  stone  with  bearing  trees;  (e)  post  in 
mound!  of  earth;  (f)  post  in  mound  of  stone;  (g)  post  with 
bearing  trees;  (h)  simple  mound  of  earth  or  stone;  (i)  tree 
without  bearing  trees;  (j)  tree  with  bearing  trees;  (k)  rock 
in  place,  etc.  The  trees  on  line  are  required  to  be  blazed. 
The  size,  markings  and  proper  corners  to  be  used  in  any 


154  LAND  SURVEYING. 

particular  case  and  all  other  details  are  given  in  the 
"Manual  of  Surveying  Instructions  for  the  Survey  of  Pub- 
lic Lands  of  the  United  States,"  issued  by  the  General  Land 
Office,  Washington,  D.  C. 

Restoration  of  Lost  or  Obliterated  Corners.* — An 
obliterated  corner  is  one  where  no  visible  evidence  remains 
of  the  work  of  the  original  surveyor  in  establishing  it.  Its 
location  may,  however,  have  been  preserved  beyond  all 
question  by  acts  of  landowners,  and  by  the  memory  of  those 
who  knew  and  recollect  the  true  position  of  the  original 
monument.  In  such  cases  it  is  not  a  lost  corner. 

A  lost  corner  is  one  whose  position  can  not  be  determined 
beyond  reasonable  doubt,  either  from  original  marks  or  re- 
liable external  evidence. 

General  Rules. — The  following  rules  are  derived  from  a 
brief  synopsis  of  congressional  legislation  relating  to  sur- 
veys. 

(1)  The  boundaries  of  the  public  lands  established  and 
returned  by  the  duly  apponted  government  surveyors,  when 
approved  by  the  surveyors  general  and  accepted  by  the  gov- 
ernment, are  unchangeable. 

(2)  The  original  township,  section,  and  quarter-section 
corners  established  by  the  government  surveyors  must  stand 
as  the  true  corners  which  they  were  intended    to    represent, 
whether  the  corners  be  in  place  or  not. 

(3)  Quarter-quarter  corners  not  established  by  the  gov- 
ernment surveyors  shall  be  placed  on   the  straight  lines 
joining  the  section  and  quarter-section  corners  and  mid- 
way between  them,  except  on  the  last  half  mile  of  section 
lines   closing  on   the   north   and   west   boundaries   of   the 
townships,  or  on  other  lines  between  fractional  sections. 

(4)  All  subdivisional  lines  of  a  section  running  between 
corners  established  in  the  original  survey  of  a  township 
must  be  straight  lines,  running  from  the  proper  corner  in 
one  section  line  to  its  corresponding  corner  in  the  opposite 
section  line. 

(5)  That  in  a  fractional  section  where  no  opposite  corre- 
sponding corner  has  been  or  can  be  established,  any  re- 

*Circular  on  the  "Restoration  of  Lost  and  Obliterated 
Corners  and  Subdivision  of  Sections,"  General  Land  Office, 
Washington,  D.  C. 


UNITED  STATES  LAND  SURVEYS. 

s 


155 


Fig.  37. 

quired  subdivision  line  of  such  section  must  be  run  from  the 
proper  original  corner  in  the  boundary  line  due  east  and 
west,  or  north  and  south,  as  the  case  may  be,  to  the  water 
course,  Indian  reservation,  or  other  boundary  of  such  sec- 
tion, with  due  parallelism  to  section  lines. 

Locations  of  Principal  Meridians. — Principal  merid- 
ians have  been  established  as  the  needs  of  the  surveys 
warranted.  The  surveys  in  the  state  of  Indiana  were  made 
with  reference  to  the  2nd  Principal  Meridian,  and  those  of 
Illinois  with  reference  to  the  2nd,  3rd  and  4th  Principal 
Meridians.  See  Pig.  37.  There  are  twenty-four  principal 
meridians  in  all,  the  locations  of  which  are  given  in  the 
"Manual  of  Instructions,"  mentioned  above. 

Abridging  Field  Notes.— The  government  surveyors  use 


156 


LAND  SURVEYING. 


the  method  of  abridging  field  notes  shown  in  Fig.  38.  Cor- 
ners in  the  township  boundary  are  referred  to  by  letter; 
interior  section  corners  are  referred  to  by  giving  the  num- 
bers of  the  sections  meeting  at  the  corner;  interior  quarter 
section  corners  are  referred  to  by  giving  the  number  on  the 
section  lines  produced. 


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Fig.  38. 
SURVEYS  BY  METES  AND  BOUNDS. 

That  portion  of  the  United  States  settled  before  the  adop- 
tion of  the  rectangular  system  was  surveyed  by  the  method 
of  metes  and  bounds.  For  the  most  part  these  surveys  were 
very  irregular  and  often  involved  complex  and  conflicting 
conditions.  The  entire  eastern  portion  of  the  United  States, 
and  the  state  of  Kentucky,  were  surveyed  in  this  manner, 
and  further  examples  are  found  in  the  French  surveys  in  the 
states  of  Michigan,  Indiana,  Illinois,  Missouri,  Louisiana, 


PROBLEMS. 


1R7 


etc  .  and  the  Spanish  surveys  of  Texas,  California,  etc.  The 
general  principles  underlying  the  questions  of  ownership, 
priority  of  survey,  the  restoration  of  lost  corners,  etc.,  are 
identical  whatever  the  system  of  survey  used. 

PROBLEMS  IN  LAND  SURVEYING. 
PROBLEM  Fl.   INVESTIGATION  OF  A  LAND  CORNER 

(a)  Equipment. — Digging  outfit,  tape,  etc,  as  required. 

(b)  Problem.— Collect  complete  evidence  relative  to  an  as- 
signed land  corner,  and  after  giving  due  weight  to  the  same, 
make  a  decision  as  to  the  true  corner. 

(c)  Metlwds. — (1)  Make  careful  examination  of  the  official 
field  notes  and   records   pertaining  to   the  land  corner  in 
question  and  make  extracts  from  the  same  for  further  ref- 
erence.    (2)  Seek  oral  evidence  from  those  acquainted  with 
the  history  of  the  corner.     (3)  Make  a  survey  of  fence  lines 
and  other  physical  evidence,  such  as  witness  trees  or  their 
stumps,  etc.,  near  the  corner  under  investigation.     (4)  Make 
careful  examination  of  the  site  of  the  corner  with  the  dig- 
ging outfit;  the  digging  should  be  done  cautiously  so  as  to 


INVESTIGATION    OF    S.W.  CORNER 


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no*  far  ~,o~y    yfon.    Alovt  /Oft 


158 


LAND  SURVEYING. 


avoid  disturbance  of  existing  stakes  or  other  monuments. 
(5)  If  more  than  one  monument  be  found,  make  due  record 
of  their  character  and  positions,  and  make  further  inquiry 
respecting  them.  (6)  If  no  monument  of  any  sort  be  found 
at  first,  continue  the  search  diligently  and  do  not  give  up 
finding  the  true  corner  as  long  as  there  is  a  remote  chance 
of  locating  it.  In  any  event,  avoid  wanton  disturbance  of 
any  object  or  evidence  that  may  have  a  bearing  on  the  same. 
Keep  clear  and  concise  record. 

PROBLEM  F2.  PERPETUATION  OF  A  LAND  CORNER. 

(a)  Equipment. — Digging  outfit,  a  large  boulder  or  other 
permanent  monument,  cold    chisel,    hatchet,    plumb    bob, 
string,  stakes. 

(b)  Problem. — Replace  a  temporary  land  corner  by  a  per- 
manent monument. 

(c)  Methods. — (1)  Uncover  the  identified  temporary  monu- 
ment and  carefully  determine  the  true  point  with  consist- 
ent exactness.     (2)  Reference  out  the  point  by  driving  two 
pairs    of    stakes    with    strings    stretched    so    as    intersect 
squarely  over  the  corner. .  (3)  After  carefully  checking  the 


ON   sec-n,  ns.. 


~tl,ct,  Htyl>   Snafttr  My,  At  Hn,M    ft  AM 
tot  ctr  ftr  over  3O  ytari .    MarHtd! 

n*f/f,  tfra.aiifm,  S-ffw.,  7r /Hi.   , 
turr-ffH,!!.         .        ft+JW.,  I2J    . 

ptfary  stoXa  evrry  10  cAt.  in  /int. 


J  R   COMINOS     AND    H.  ROWLAND. 


r  traflt   ot  corrrLt  point, 
f  frtt  ef  OJ.  Jvrvt},  timir.g 


flftet    of  T  r&l  £4  ins.  forty  art  fop 
M.C.KH.    norm  ao~r. 


rt  sfmf.t 


PROBLEMS.  159 

referencing,  dig  out  the  old  monument  to  a  depth  sufficient 
to  receive  the  boulder  and  permit  its  top  to  set  several 
inches  beneath  the  natural  siirface  if  located  in  a  road  or 
where  disturbance  is  probable.  (4)  Cut  a  plain  cross  mark 
on  the  top  of  the  stone,  and  set  it  in  place  in  the  hole, 
packing  the  earth  about  it,  and  testing  the  position  of  the 
mark  by  means  of  the  reference  stakes  and  strings  and 
plumb  bob;  finally  leave  the  boulder  set  firmly  in  the  correct 
position.  (5)  Make  reference  measurements  to  suitable  per- 
manent points  such  as  marks  on  curbing,  gas  pipes,  witness 
trees,  etc.,  selected  with  respect  to  good  intersections,  and 
make  reliable  record  of  the  witness  notes  after  checking 
the  same.  (Other  forms  of  permanent  monuments  are: 
gas  pipe;  fish  plate;  section  of  T-rail;  farm  tile  or  vitri- 
fied pipe  filled  with  cement  mortar;  post  hole  filled  with 
mortar;  special  solid  monument  burned  like  farm  tile; 
special  casting  similar  to  a  gas  main  valve  box,  with  hole 
in  top  to  receive  flag  pole;  etc.) 

PROBLEM    F3.      REESTABLISHING    A    QUARTER-SEC- 
TION CORNER. 

(a)  Eq ii ivnirnt—  Transit  party  outfit,   digging  tools,  etc. 

(b)  TVoWfw?.— Reestablish   a  quarter-section   corner  that 
has  been  obliterated  or  lost. 

(c)  MrtJind .<?.—(!)  Collect  and  record  all  the  available  evi- 
dence which  may  assist  in  the  discovery  and  identification 
of  the  corner.    Examine  the  field  notes  of  the  original  sur- 
vey, the  surveyors'  plat  book  and  the  county  atlas  on  file 
at  the  court  house,  and  make  diligent  inquiry  for  credible 
and  competent  information,  either  written  or  oral  as  to  the 
location  of  the  corner.     (2)  Make  a  careful  search  for  the 
monument.    Trace  all  the  lines  of  the  original  survev.  nav- 
ing  particular  attention  to  bearing  and  sight  trees.     Dig  in 
all  the  places  indicated  by  the  different  lines  and  give  un 
the  search   only  after  you  have  exhausted  every  possible 
flue.     (3)  If  the  corner  cannot  be  found,  reestablish  it,  giv- 
ing due  weight  to  all  the  evidence.     The  surveyor  should 
remembpr  -fhat  the  corner  should  be  reestablished  where  it 
originally  was  and  not  where  it  ought  to  be.    After  having 
located   a  stake   at  the  supposed  location   of   the  original 
monument   .reference  it  out  and   renew   the   search.      (4) 


160  LAND  SURVEYING. 

After  the  monument  has  been  relocated ,  mark  it  in  a  per- 
manent manner  as  indicated  in  Problem  F2,  by  a  stone 
with  a  cross  cut  in  its  top  or  with  a  gas  pipe  well  driven 
into  the  ground.  Reference  it  out  to  at  least  two  permanent 
ofbjeets  selected  with  a  view  to  securing  a  first  class  inter- 
section. Make  a  careful  record  and  preserve  consistent  ac- 
curacy in  the  work. 

PROBLEM  F4.  REESTABLISHING  A  SECTION  CORNER. 

(a)  Equipment. — Transit  party  outfit,  digging  tools,  etc. 

(b;  Problem. — Reestablish  an  obliterated  or  lost  section 
corner. 

(c)  Method*. — Follow  the  various  methods  described  in 
Problem  F3,  giving  special  attention  to  the  search  for  the 
original  corner;  upon  failing  to  find  trace  of  it,  run  out  lines 
with  reference  to  the  section,  quarter,  and  quarter-quarter 
corners  in  the  four  directions,  with  linear  measurements 
from  the  same  and  finally  reach  the  most  consistent  de- 
cision with  reference  to  such  survey  lines,  ownership  lines, 
fences,  hedges,  road  centers,  etc.  (A  fruitful  cause  of  dis- 
turbance of  section  'and  other  corners  is  careless  use  of 
road  graders,  or  the  failure  to  lower  the  corner  sufficiently 
below  the  surface  of  the  road.) 

PROBLEM  F5.     RESURVEY  OF  A  SECTION. 

(a)  Equipment. — Transit  party  outfit,  digging  tools,  etc. 

(b)  Problem. — Make  a  resurvey  of  an  assigned  section. 

(c)  ^fetllods.—'(l)  Make  extracts  from  the  field  notes  of 
the  original  survey  and  of  all  resurveys  on  file  at  the  court 
house,  and  other  notes  that  may  be  of  value.     Make  dili- 
gent inquiry  among  the  property  owners  fpr  evidence  as  to 
the  location  of  corners.  (2)  Retrace  the  lines,  recording  the 
location  of  old  fences,  timber  markings  and  other  evidences 
as  to  prior  recognition  of  lines  and  corners.    Use  consistent 
accuracy.    Record  the  original  notes  as  given  in  the  forms. 
Record  the  field  notes  in  narrative  style  using  the  designa- 
tion of  corners  as  given  in  the  resurvey  plat  in  the  form. 
Make  a  plat  of  the  section  in  the  manner  prescribed  by  state 
law  for  a  resurvey. 


PROBLEMS. 


161 


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LAND  SURVEYING. 


RESUfVEY  or  SECJ7,  T.\IH.,  R.  *Vi,3RaRM. 

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STATE      (CONTINUED) 


PROBLEMS.  163 


PROBLEM  F6.     RESURVEY  OF  A  CITY  BLOCK. 

(a)  Equipment. — Transit,    100-foot    steel    tape,    chaining 
pins,  axe,  hubs,  stakes,  4  pieces  one-inch  gas  pipe  2  feet 
long,  notes  of  previous  surveys,  etc. 

(b)  Problem. — Make  a  resurvey  of  an  assigned  city  block. 

(c)  Method*.— (1)  Procure  full  notes  of  all  the  surveys  and 
resurveys  of  the  assigned  block  from  the  records  at  the 
court  house  and  from  any  other  source  available.     (2)  Make 
a  resurvey  of  the  block,  using  the  notes,  and'  drive  hubs  for 
temporary  corners.     (3)  Compute  the  latitudes  and  depart- 
ures of  the  courses,  and  if  consistent,  balance  the  survey. 
(4)  If  the  corners  of  the  block  as  located  are  consistent  with 
the  existing  property  and  street  lines,  drive  gas  pipes  as 
permanent  corners.     (5)    Subdivide  the  block  into  lots  as 
shown  in  the  notes.     (6)  Make  a  plat  of  the  block  on  manila 
paper  to  the  prescribed  scale,  showing  block  and  lot  lines, 
distances  and  angles  obtained  in  making  the  survey,  the 
names  of  the  owners  of  the  property  and  the  names  of  the 
streets.    Prepare  a  surveyors'  certificate  as  provided  by  law. 
Trace  the  map  if  required.     (The  accuracy  attained  should 
be    based    on    the    valuation    and    other    local    conditions. 
Before  beginning  the  survey  use  every  possible  care  to  find 
the  corners  with  reference  to  which  the  original  survey  was 
made.     When  lots  are  sold  by  number,  the  excess  or  de- 
ficiency should  be  divided  pro  rata.  However,  when  lot  lines 
have  been  long  acquiesced  in,  it  is  doubtful  if  the  courts  will 
uphold  the  surveyor  in  interfering  with  the  ancient  lines  of 
ownership.     It  then  becomes  necessary  either  to  make  a 
compromise  survey  that  will  be  satisfactory  to  the  owners, 
or  to  make  a  survey  that  is  strictly  according  to  the  letter 
of  the  law,  and  submit  the  map  and  certificate  to  the  courts 
for  settlement.     The  surveyor  should  remember  that  he  is 
simply  an  expert  witness  and  that  he  has  no  final  judicial 
powers.) 

PROBLEM  F7.  RESURVEY  BY  METES  AND  BOUNDS. 

(a)  Equipment.— Transit  party  outfit,  digging  tools,  etc. 

(b)  Problem. — Make  a  resurvey  of  an  assigned  tract  whose 
original  survey  was  made  by  metes  and  bounds. 


164  LAND  SURVEYING. 

(c)  Methods. — (1)  Collect  full  notes  and  data  relating  to 
the  monuments,  magnetic  bearings,  magnetic  variation, 
date  of  survey,  lengths  of  lines,  etc.  (2)  Make  a  careful 
investigation  of  the  lines  and  corners  on  the  ground  and 
make  notes  of  any  evidence  there  found.  (3)  Locate  and 
identify  with  certainty  as  many  as  possible  of  the  original 
monuments;  where  double  or  contested  corners  exist,  locate 
each  definitely  for  further  reference;  if  corners  are  general- 
ly lacking  or  doubtful,  concentrate  attention  on  at  least  two 
which  give  most  promise  of  definite  relocation,  and  reestab- 
lish these  corners  as  carefully  as  possible.  (4)  Having  at 
least  two  corners,  retrace  by  random  line  the  perimeter  of 
the  tract  according  to  the  original  description,  beginning 
at  one  and  closing  on  the  other  corner;  set  temporary  cor- 
ner stakes  at  the  several  points;  note  the  linear  and  angular 
error  of  closure  of  the  random  traverse  on  the" last  monu- 
ment. (5)  Calculate  the  latitudes  and  departures  of  the 
random  survey,  and  determine  the  angular  and  linear  re- 
lations between  the  random  and  the  original  survey;  also 
fix  the  position  of  the  several  random  stakes  relative 
to  the  supposed  true  positions  of  the  respective  corners.  (6) 
Set  stakes  in  the  true  positions,  as  calculated,  reference 
them  out,  and  renew  the  search  for  the  original  monu- 
ments. (7)  Finally  reestablish  each  corner  in  the  most 
consistent  position,  put  permanent  corners  in  place,  and 
take  witness  notes  for  each,  making  complete  notes  of  the 
proceedings.  Follow  form. 


PROBLEM  F8.     PARTITION  OF  LAND. 


(a)  Equipment.— Transit  party  and  digging  outfits,  etc. 

(b)  Problem. — Make  a  partition  of  an  assigned  tract  of 
land  in  accordance  with  instructions. 

(c)  Methods. — (1)  Make  the  necessary  resurveys  of  the  as- 
signed tract,  identifying  original  monuments,  and  reestab- 
lishing lost  corners  as  required.     (2)   Make  a  plat  of  the 
partition.     (3)  Subdivide  the  land  and  set  permanent  cor- 
ners; carefully  establish  witnesses  to  the  corners  and  secure 
witness  notes.     (4)  Prepare  and  file  plat  and  description  as 
required  by  law. 


PROBLEMS. 


165 


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166  LAND  SURVEYING. 

PROBLEM  F9.    DESIGN  AND  SURVEY  OF  A  TOWN  SITE 
(OR  ADDITION.) 

(a)  Equipment. — Equipment   for   topographic    survey   for 
both  field  and  office. 

(b)  Problem.— Make  a  preliminary  topographic  survey  of 
the  proposed  town  site  (or  addition)   design  the  plat,  and 
make  the  surveys  for  blocks,  lots,  etc. 

(c)  Methods. — (1)   Make  a  careful  resurvey  of  the  entire 
tract.    Reference  the  existing  monuments  and  carefully  re- 
locate all  mis-sing  corners.     (2)  After  the  monuments  have 
been  carefully  located,  remeasure  the  distances  and  angles 
very  carefully.    Before  beginning  the  chaining,  a  standard 
should    be    established     as     described'    in    Problem    A23. 

(3)  Fill  in  the  topographic  details  with  the  transit  and 
stadia,  unless  directed  otherwise,  using  consistent  accuracy. 

(4)  Make  a  complete  topographic  map  of  the  tract.     (5)  De- 
sign the  townsite  and  sketch  it  in  on  the  map.    The  ques- 
tions  of  surface    drainage,    sewerage,    possible    overflow, 
street  gradients,  principal  thoroughfares,  diagonal  streets, 
alleys,   etc.,  should   be   carefully   considered.     The  streets 
should  be  of  ample  width  and  laid  out  with  reference  to  ease 
of  grading  both  the  Street  and  the  adjacent  property.    Resi- 
dences should  face  desirable  streets  and  the  cross  streets  in 
the  residence  district  should  not  be  too  numerous.     The 
principal  thoroughfare  should   pass  through   the  business 
portion  and  have  minimum  gradients.    The  system  of  sew- 
erage and  drainage  Should  be  worked  out  roughly  before 
the  design  is  completed.    Much  expensive  construction  can 
be  avoided  by  using  care  in  designing  the  town  site.     (6) 
Make  preliminary  profiles   of  all  the  streets   on   Plate   A 
profile  paper  to  the  prescribed  scale.     (7)  Carefully  locate 
the  block  and  other  important  corners  and  mark  them  by 
permanent  monuments  of  stone,  gas  pipe,  tiling,  etc.     (8) 
Subdivide  the  blocks  into  lots  and  mark  the  lot  corners  by 
means  of  gas  pipes  or  hubs.    (9)  After  the  streets  have  been 
located  carefully,  take  levels  on  the  same,  make  profiles, 
and  lay  grade  lines  for  all  streets,  sidewalks,  and  improve- 
ments. 

Use  accuracy  consistent  with  the  value  of  the  property 
throughout  the  problem.  Make  a  careful  record  of  the  notes. 
Complete  the  maps  and  profiles. 


CHAPTER  VIII, 
RAILROAD  SURVEYING, 


Classification  — For  the  purpose  of  class  instruction, 
railroad  surveying  will  be  discussed  under  the  following 
heads:  (1)  curve  practice,  (2)  reconnaissance,  (3)  prelim- 
inary survey,  (4)  location  survey,  (5)  construction,  (6) 
maintenance. 

Curve  practice  is  designed  to  give  the  student  familiarity 
with  the  methods  of  running  curves  so  that  the  location 
survey  may  be  made  without  needless  delay.  It  consists  of 
a  series  of  typical  problems  covering  the  usual  range  of 
conditions  found  in  such  surveys. 

The  reconnaissance  is  a  rapid  preliminary  examination 
of  a  district  or  area  for  the  purpose  of  selecting  ruling 
points  to  control  the  general  routes  of  the  preliminary  sur- 
vey lines.  The  distances  are  paced  or  scaled  from  a  map; 
elevations  are  determined  by  means  of  the  barometer  or 
hand  level. 

The  preliminary  survey  is  designed  to  obtain  information 
and  to  obtain  it  rapidly,  as  a  guide  in  making  the  location 
survey.  A  rapid  deflection  angle  traverse  is  run,  following 
the  general  route  of  the  proposed  line,  but  keeping  in  clear 
ground  as  far  as  may  be  to  gain  time;  levels  are  run,  topog- 
raphy including  contours  taken,  the  map  made,  and  one  or 
more  location  lines  projected  on  the  map. 

The  location  survey  fixes  the  exact  lines,  including  the 
curves,  preparatory  to  building  the  proposed  railroad.  Some 
engineers  prefer  to  run  one  or  more  trial  location  lines,  but 
it  is  best  practice  to  locate  the  line  as  projected  on  a  reliable 
contour  map. 

Construction  surveys  are  made  for  the  purpose  of  fixing 
the  roadbed  limits  and  other  constructive  details,  and  esti- 
mating earthwork  and  other  quantities. 

Maintenance  surveys  and  resurveys  are  made  after  the 
line  is  built,  for  ballasting,  yard  construction  or  other  pur- 
pose. 


168  RAILROAD  SURVEYING. 

Field  Organization  of  Class. — In  order  to  carry  out  the 
foregoing  steps,  the  following  field  parties  are  required: 
(a)  transit  party,  (b)  leveling  party,  (c)  topography  party, 
(d)  land-line  party,  (e)  cross-sectioning  party,  (f)  bridge 
and  masonry  party,  (g)  resurvey  party. 

General  Requirements, — Each  party  should  work  with 
snap  and  vigor  and  accomplish  the  best  results  practicable, 
both  as  to  quality  and  quantity.  To  this  end  each  member 
of  the  party  should  not  only  be  careful,  exact,  and  rapid  in 
the  discharge  of  his  own  duties,  but  avoid  interfering  with 
the  work  of  others,  such  as  obstructing  the  view  of  the 
transitman.  In  order  to  give  each  student  practice  in  all 
the  positions,  the  posts  will  be  shifted  daily,  progressing  to 
the  higher  positions  in  the  party.  The  student  should  not 
underrate  his  practice  in  the  subordinate  positions,  nor  fail 
to  make  proper  use  of  his  more  responsible  duties.  The 
usual  decorum  of  field  parties  will  be  observed. 

TRANSIT  PARTY.— It  is  the  duty  of  the  transit  party  to 
establish  the  traverse  line  upon  which  to  base  the  levels  and 
topography.  The  student  transit  party  will  consist  of  the 
following  members:  (1)  chief  of  party,  (2)  transitman,  (3) 
head  chainman,  (4)  rear  chainman,  (5)  stakeman,  (6)  axe- 
man, (7)  front  flagman,  (8)  rear  flagman.  The  duties  and 
equipment  of  the  respective  members  are  stated  below. 

Chief  of  Party. — (Party  list,  map  of  line,  50-foot  metallic 
tape,  railroad  curve  text  book.)  The  chief  of  party  is  re- 
sponsible for  the  general  progress  and  quality  of  the  work. 
It  is  his  duty  to  direct  the  survey;  see  that  each  man  does 
his  work  properly  and  with  sufficient  accuracy  and 
despatch;  check  the  transitman's  work  when  necessary; 
keep  the  transit  notes  if  the  transitman  is  pushed;  and  make 
himself  generally  useful.  He  should  be  thoroughly  ac- 
quainted, before  going  to  the  field,  with  the  situation  and 
with  the  data  applicable  to  the  work  of  the  day.  In  requir- 
ing subordinate  members  of  the  party  to  perform  their  work 
properly,  he  should  carefully  preserve  the  dignity  of  his 
own  position.  Should  there  be  no  chief,  these  duties  will  be 
shared  by  the  transitman  and  head  chainman  under  the 
former's  directions. 

Transitman. — (Transit,  reading  glass,  adjusting  pin, 
transit  note  book,  railroad  curve  text  book,  figuring  pad.) 
The  transitman  runs  the  transit,  keeps  the  notes,  and  in 


TRANSIT  PARTY.  169 

the  absence  of  the  chief,  directs  the  work  of  the  party.  He 
should  do  careful  and  exact  as  well  as  rapid  work,  since  the 
progress  and  character  of  the  survey  are  usually  controlled 
chiefly  by  the  skill  of  the  transitman. 

In  leveling  up,  keep  the  lower  parallel  plate  about  level. 
Avoid  undue  tightness  of  foot  screws.  In  setting  the  ver- 
nier to  zero,  use  a  quick  converging  motion  with  the  tangent 
movement  and  note  the  adjacent  graduations.  If  the  (tran- 
sit has  lost  motion,  learn  which  way  to  get  the  slack  on  the 
tangent  screws.  As  a  rule,  use  the  lower  motion  by  prefer- 
ence. Habitually  back  sight  to  the  rear  with  telescope  re- 
versed, then  plunge  the  telescope  on  prolongation  and  read 
the  deflection  right  or  left.  If  practicable,  base  tfhe  cal- 
culated bearings  on  a  true  meridian;  otherwise,  allow  for 
the  magnetic  declination  at  a  station  which  seems  to  be  free 
from  local  attraction  and  thus  obtain  a  reference  meridian. 
Check  all  deflection  angles  by  needle  reading,  both  as  to 
amount  and  direction.  Lack  of  proper  adjustment  is  no 
excuse  for  error.  Always  prolong  a  tangent  line  by  double 
sightings.  Also  check  deflection  angles  from  time  to  time, 
by  double  sightings.  Check  on  back  sight  before  finally 
approving  any  precise  point;  likewise  never  fail  to  conclude 
the  observations  at  each  transit  station  by  checking  on  the 
back  sight.  In  such  check  it  is  usually  best  to  sight  hack 
precisely  on  the  point  and  then  note  whether  the  vernier  has 
the  proper  reading.  Assist  the  flagman  in  plumbing  the 
pole,  and  always  sight  as  near  the  bottom  of  the  pole  as 
possible.  The  traisitman  should  admonish  the  chainmen, 
etc.,  to  keep  clear  of  the  line. 

On  preliminary  surveys,  usually  let  the  rear  chainman 
line  in  the  head  ohainman  by  eye,  at  least  for  short 
stretches.  Do  not  hesitate  to  offset  or  zig-zag  more  or  less 
along  open  ground  to  gain  time.  A  rapid  method  for  pass- 
ing through  heavy  timber  is  to  zig-zag  on  slight  deflection 
angles  right  and  left,  tabulate  the  lengths  in  stations  and 
deflections  in  minutes,  and  the  products  of  the  two  in  sep- 
arate columns  on  the  right  hand  page.  The  original  line  is 
regained  by  making  the  algebraic  sum  of  the  products  zero, 
and  the  original  direction  is  resumed  by  turning  off  a  de- 
flection which  balances  the  deflection  angle  columns. 

On  location,  each  stake  should  be  lined  in  carefully  by 
transit.  Small  obstructions,  such  as  trees,  may  be  passed 


170  RAILROAD  SURVEYING. 

by  parallel  lines,  using  offsets  of  one  foot  or  so  at  two  hubs 
a  few  stations  apart;  the  line  is  resumed  in  like  manner. 
Where  plate  readings  are  used  in  rectangular  or  other  offset 
methods,  no  sights  shorter  than  50  feet  should  be  used.  The 
equilateral  triangle  one  station  or  more  on  a  side  is  often 
used.  Obstructions  on  curves  may  usually  be  passed  readily 
with  the  aid  of  tables  of  long  chords  and  mid-ordinates. 

Curve  index-readings  should  be  calculated  as  though  the 
entire  curve  were  to  be  run  in  from  the  P.  C.;  starting  with 
the  index-reading  of  P.  C.  always  equal  to  zero,  check  the 
calculations  by  noting  that  the  index  of  M.  C.  is  *4  I,  and  of 
P.  T.  is  %  I.  In  using  the  notes,  remember  that  with  the 
transit  at  any  point  whatever  on  the  curve  the  following 
rules  apply:  (1)  When  pointing  to  any  station,  the  ver- 
nier must  always  be  set  to  read  the  index-reading  for  that 
station;  and  (2)  when  pointing  on  tangent  at  any  station, 
the  vernier  must  be  set  to  read  the  index-reading  for  that 
station.  As  a  rule,  the  best  program  in  curve  location  is: 
Having  P.  I.  located,  (1)  measure  I  and  assume  D;  (2)  cal- 
culate T  and  E;  (3)  establish  P.  T.  by  chaining  off  T  on 
front  tangent;  (4)  establish  M.  C.  by  laying  off  E  on  bisect- 
ing line;  (5)  locate  P.  C.  by  interpolating  hub  at  calculated 
station  number  on  back  tangent;  (6)  move  transit  to  P.  C. 
and  fore  sight  on  P.  I.;  (7)  calculate  curve  notes  (if  not  al- 
ready done);  (8)  check  sight  on  P.  T.  and  M.  C.  and  if  satis- 
factory, (9)  run  in  curve,  checking  for  distance  and  angle  on 
M.  C.  and  P.  T.,  moving  transit  ahead  if  desirable  or  neces- 
sary; (10)  set  up  at  P.  T.  and  resume  front  tangent.  One 
minute  is  the  limit  of  allowable  error  in  any  curve.  Mis- 
takes in  calculations  or  in  measurements  of  angles  will  be 
counted  serious  errors.  On  final  location  the  curves  will  be 
spiraled.  After  the  line  is  located,  reference  out  P.  C.,  P.  T., 
and  other  important  hub  points  by  two  intersecting  lines 
and  take  careful  notes  of  the  same  (see  method  (g),  Fig.  5, 
Chapter  II.) 

The  transit  notes  should  be  reliable,  complete,  neat  and 
distinct.  Each  entry  should  have  but  one  reasonable  mean- 
ing and  that  the  correct  one.  Record  station  numbers  from 
the  'bottom  upwards,  usually  with  ten  stations  per  page. 
Repeat  the  last  station  at  the  top  of  the  next  page.  Allow 
two  lines  per  station  so  as  to  provide  for  sketching  at  200 
feet  to  the  inch.  On  the  middle  line  of  the  right  hand  page 


TRANSIT  PARTY. 


171 


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10AO     LOCATION     SI  RVEY.) 


172  RAILROAD  SURVEYING. 

mark  each  station  with  a  dot  and  number  every  fifth  station 
which  should  also  be  enclosed  in  a  circle.  The  transit  notes 
should  include  sketches  of  prominent  land  and  street  lines, 
stream  crossings  and  other  prominent  topographic  details, 
with  pluses  shown  in  the  sketch.  The  notes  should  include 
date,  weather,  organization  of  party,  etc.  An  appropriate 
title  page  giving  name  of  survey,  date  of  commencement 
and  completion,  etc.,  should  be  prepared.  The  notes  will  be 
kept  in  the  prescribed  form.  The  field  notes  are  to  be  re- 
turned at  the  close  of  the  day's  work.  All  estimated  data 
should  be  noted  as  such. 

Completeness  and  neatness  of  notes  and  records,  facility 
and  accuracy  in  handling  the  instrument,  and  promptness 
in  advancing  the  progress  of  the  survey  will  count  in  the 
estimate  of  the  work  of  the  transitman. 

Head  Chainman. —  (Flag  pole.)  The  progress  of  the 
chaining  depends  chiefly  on  the  activity  of  the  head  chain- 
man.  After  setting  a  stake  he  should  move  off  briskly  (pre- 
ferably at  a  trot)  and  be  prepared  for  the  "halt"  signal  as 
he  approaches  the  next  station.  When  the  full  chain  length 
is  pulled  out,  the  head  chaimman  turns,  holding  the  flag  pole 
in  one  hand  and  the  chain  handle  in  the  other,  and  sets  the 
pole  in  line  by  signal  from  the  rear  chainman  01  transit- 
man. Much  time  can  be  saved  in  this  process  if  the  head 
chainman  habitually  walks  about  on  line  and  if  he  sights  back 
over  the  two  stakes  last  set.  If  on  curve  location,  he  should 
line  himself  in  on  the  prolongation  of  the  preceding  station 
chord,  and  then  offset  by  pacing  or  with  flag  pole  a  distance 
in  feet  equal  to  1%  times  the  degree  of  the  curve;  the 
calculation  is  made  mentally  and  the  pole  can  usually  be  set 
within  a  few  inches  of  the  correct  position  by  the  time  a 
speedy  transitman  has  the  deflection  angle  set  off.  Having 
the  line  established,  the  pole  is  shifted  to  the  correct  dis- 
tance, and  the  stake  is  driven  plumb  in  the  hole  made  by 
the  flag  pole  spike.  If  the  survey  is  a  rapid  preliminary  line, 
the  head  chainman  hastens  ahead  the  instant  the  stake  is 
started  at  the  proper  point,  although  in  a  more  careful  pre- 
liminary the  chainmen  check  the  distance  to  the  driven 
steke.  On  location  surveys  it  is  customary  for  the  chain- 
men  to  wait  until  the  stake  is  driven  and  mark  the  exact 
distance  on  the  top  of  the  stake  with  the  axe  blade,  and  the 
exact  line  by  signal  from  the  transitman.  In  this  process, 


TRANSIT  PARTY.  173 

the  head  chainman  should  keep  in  mind  the  convenience  of 
the  transitman,  and  in  case  the  line  is  being  run  to  a  front 
flag,  the  chainman  should  be  careful  to  clear  the  line  fre- 
quently to  allow  check  sights  ahead.  In  breaking  chain  on 
steep  slopes  the  full  length  of  chain  should  usually  be  pulled 
out  ahead  and  the  chain  thumbed  at  the  breaking  points  so 
as  to  avoid  blunders;  a  plumb  bob  or  flag  pole  should  be 
used  in  the  process.  In  passing  over  fences  it  often  saves 
time  to  drive  a  10-d  nail,  with  "butterfly"  attached,  in  the 
top  plank  to  serve  as  a  check  back  sight  from  the  next  tran- 
sit point.  The  chainmen  should  carefully  avoid  obstruct- 
ing the  transitman's  view,  to  which  end  they  should  walk 
on  the  outside  when  locating  curves. 

Rear  Chainman. — (100-foot  chain  or  tape,  chaining  pins 
(if  allowed),  figuring  pad  or  note  book.)  As  the  rear  chain- 
man approaches  the  stake  just  set,  he  calls  out  "halt"  and 
holds  the  end  of  the  chain  approximately  over  the  stake. 
quickly  lines  in  the  flag  pole  in  the  hand  of  the  head  chain- 
man (or  the  pole  is  lined  in  by  the  transitman).  the  precise 
distance  is  given,  and  the  chainmen  move  on  briskly.  As  a 
rule,  pluses  should  be  read  by  the  rear  chainman,  the  front 
end  being  held  at  the  point  to  be  determined.  Frac- 
tions will  usually  be  taken  to  the  nearest  01  foot,  although 
0  01  foot  may  at  times  be  properly  noted.  It  is  the  duty  of 
the  rear  chainman  to  keep  a  record  of  pluses  and  tooo- 
graphic  details  when  the  transitman  is  not  at  hand.  This 
record  may  be  kept  on  a  figuring  pad  and  the  memoranda 
handed  at  the  first  opportunity  to  the  transitman,  who 
transfers  the  data  to  his  book  and  carefully  preserves  the 
slips  for  future  reference.  It  is  usually  better,  however,  to 
keep  the  auxiliary  notes  in  a  memorandum  book  instead  of 
on  the  loose  slips.  The  chainmen  should  carefully  avoid 
disturbing  the  transit  legs. 

The  responsibility  for  correct  numbering  of  the  station 
stakes  rests  chiefly  on  the  rear  chainman.  It  is  his  duty 
to  remember  the  number  of  the  previous  station  so  as  to 
catch  blunders  on  the  part  of  the  stakeman.  As  he  reaches 
the  stake  just  driven,  he  mentally  verifies  its  number  and 
repeats  it  distinctly  for  the  guidance  of  the  fetakeman  in 
marking  the  stake  to  be  driven:  the  stakeman  responds  by 
calling  the  new  number,  and  each  repeats  his  number  as  a 
check  before  final  approval.  The  rear  chainman  then 


174  RAILROAD  SURVEYING. 

charges  his  mind  with  the  numbers  and  checks  the  newly 
set  stake  on  reaching  it.  In  case  of  doubt  he  returns  to  the 
preceding  stake  and  notes  its  number. 

Stakeman.—  (Sack  of  flat  and  hub  stakes,  marking 
crayon,  handaxe.)  The  stakeman  with  his  supply  of  flat  and 
hub  stakes  in  a  sack,  should  keep  up  with  the  head  chain- 
man  and  be  standing,  with  stake  and  marking  keel  in  hand, 
ready  to  number  the  new  station  stake  on  hearing  the  rear 
chainman  call  out  the  preceding  station  number;  the  num- 
bering is  repeated,  as  already  explained,  before  the  stake  is 
driven.  Chaining  pins  are  not  used,  but  their  equivalent  in 
checking  tallies  may  be  had  by  numbering  the  stakes  ahead 
and  tieing  them  up  in  sets  of  ten.  By  numbering  stakes  at 
slack  moments  the  stakeman  gains  time  to  assist  the  axe- 
man in  clearing  the  line,  etc.  However,  special  care  should 
be  taken  to  avoid  omissions  and  duplicates.  The  stakeman 
should  finish  numbering  the  stake  and  hand  it  to  the  axe- 
man by  the  time  the  head  chainman  has  fixed  the  exact 
station  point.  The  stakes  should  be  numbered  in  a  bold  and 
legible  manner,  the  keel  being  pressed  into  the  wood  for 
permanency.  The  number  should  read  from  the  top  of  the 
stake  downward.  Stakes  on  an  offsetted  line  should  be  so 
marked,  as  4'L  or  2'R,  beneath  the  station  number.  When 
survey  lines  are  lettered,  the  serial  letter  should  precede  the 
station  number.  Guard  stakes  for  P.  I.,  P.  C.,  P.  T..  refer- 
ence points  (R.  P.),  etc.,  should  be  clearly  marked.  The 
stakeman  should  assist  the  axeman  in  clearing  the  line  and 
should  drive  stakes  when  the  axeman  is  delayed.  He  should 
carefully  avoid  obstructing  the  transitman's  view.  The 
s<takeman  is  under  the  direction  of  the  head  chainman. 

Axeman. — (Axe,  tacks.,  (and  if  so  instructed)  an  extra 
sack  of  stakes  with  marking  keel.)  It  is  the  duty  of  the  axe- 
man to  drive  stakes,  remove  underbrush  from  the  line, 
clear  an  ample  space  about  the  transit  station,  etc.  He  is 
expressly  warned,  however,  in  student  field  practice,  not  to 
hack  or  cut  trees  or  damage  other  property  in  any  way,  and1 
in  general,  not  to  trespass'  on  the  rights  of  owners  of 
premises  entered  in  the  progress  of  the  survey. 

The  flat  station  stakes  are  driven  firmly  crosswise  to  the 
linje  with  the  numbered  face  to  the  rear.  Hubs  are  driven 
about  flush  and  usually  receive  a  tack;  they  are  properly 
witnessed  by  a  flat  guard  stake  driven  10  inches  or  so  to  the 


TRANSIT  PARTY.  175 

left,  the  marked  face  slanting  towards  the  hub,  as  shown 
in  Fig.  9,  Chapter  II.  The  axeman  receives  the  marked 
stake  from  the  stakeman  and  drives  it  plumb  at  the  point 
marked  by  the  spike  of  the  flag  pole.  On  location  or  care- 
ful preliminary  surveys  when  the  stakes  are  being  lined  in 
by  transit,  the  axeman  should  stand  on  one  side  when  driv- 
ing and  keep  a  lookout  for  signals  from  the  transitman.  In 
shifting  the  stake  as  signaled  he  should  use  combined  driv- 
ing and  drawing  blows  with  the  axe.  When  the  precise 
point  comes  much  to  one  side  of  the  top  of  the  hub,  another 
hub  should  be  driven  alongside  and  the  first  one  driven  out 
of  sight  before  the  tack  is  set.  The  axeman  should  move 
ahead  briskly  and  avoid  delay  to  the  chaining.  The  stake- 
man should,  when  necessary,  drive  the  stake  with  the  spare 
handaxe.  When  the  field  force  is  scant,  one  man  may  serve 
in  "both  capacities.  The  axeman  is  under  the  direct  charge 
of  the  head  chainman. 

Front  Flagman.— (Flag  pole,  small  supply  of  hubs  and 
guard  stakes  in  stake  sack,  handaxe,  a  few  10-d  nails.)  It 
is  the  duty  of  the  front  flagman  to  establish  hub  points 
ahead  of  the  chaining  party  under  the  direction  of  the  chief 
and  transitman.  In  selecting  transit  stations  he  should 
keep  in  mind  visibility  and  length  of  both  fore  sight  and 
back  sight,  and  to  this  end,  points  should  be  taken  on  ridge 
lines  and  where  underbrush,  etc..  is  least  in  the  way.  The 
practice  of  planting  the  flag  pole  behind  the  hub  may  be 
warranted  occasionally,  as  for  example,  when  the  field 
party  is  shorthanded,  but  never  when  the  regular  flagman 
is  not  specially  detailed  for  other  duties.  The  front  flagman 
should  keep  close  watch  on  the  transitman  and  should 
habitually  stand  with  the  spike  of  the  flag  pole  on  the  tack 
head  and  plumb  the  pole  by  standing  squarely  behind  it 
and  supporting  it  between  the  tips  of  the  fingers  of  the  two 
hands.  Should  the  front  flagman  be  flagging  for  an  inter- 
polated point  depending  on  a  foresight  which  his  pole  would 
conceal,  he  should  clear  the  line  for  a  check  sight  by  lean- 
ing the  pole  to  'one  side.  When  crossing  fences  he  should, 
when  convenient,  establish  check  sights  on  the  top  plank 
by  driving  a  spike  and  attaching  a  "butterfly." 

Rear  Flagman. — (Flag  pole,  hatchet,  slips  of  paper.)  T^he 
rear  flagman  gives  back  sight  on  the  preceding  transit  sta- 
tion. The  details  of  his  duties  are  much  the  same  as  those 


176  RAILROAD  SURVEYING. 

of  the  front  flagman.  It  is  an  excellent  plan  for  him  to  cut 
a  straight  sappling  or  limb  and  plant  it  exactly  behind  the 
hub  when  signaled  ahead.  This  picket  pole  is  made  more 
visible  by  splitting  the  top  and  inserting  a  slip  of  paper,  to 
make  a  "butterfly."  A  series  of  such  pickets  on  a  long 
tangent  line  often  affords  a  fine  check  on  the  work  when 
an  elevated  transit  point  is  reached. 

LEVEL  PARTY. — It  is  the  purpose  of  the  level  party  to 
secure  data  concerning  the  elevations  of  the  points  along 
the  line  so  that  an  accurate  profile  may  be  made  and  the 
grade  line  established.  The  leveling  party  should  be  on  the 
alert  to  detect  errors  in  the  work  of  the  transit  party,  such 
as  omitted  or  duplicated  stations,  etc.  The  party  consists  of 
two  members:  (1)  leveler,  (2)  rodman.  In  very  brushy 
country  an  axeman  may  be  added,  but  this  is  usually  un- 
necessary if  the  line  cleared  by  the  transit  party  is  followed. 

Leveler. — (Level,  adjusting  pin,  level  note  book.)  The 
leveler  should  follow  the  most  approved  methods  described 
under  the  head  of  differential  and  profile  leveling  in  Chap- 
ter IV.  The  nearest  0.01  foot  should  be  observed  on  turn- 
ing points  and  bench  mark  rod  readings  and  elevations  and 
on  occasional  important  profile  points.  The  fore  sight  rod 
readings  on  ground  profile  points  are  to  be  taken  only  tb 
t;h«  nearest  0.1  foot  and- the  nearest  0.1  foot  in  the  height  of 
instrument  is  to  be  used  in  calculating  the  elevation.  (Be- 
ginners sometimes  calculate  elevations  to  0.01  foot  when  the 
rod  readings  are  taken  only  to  the  nearest  0.1  foot.)  The 
leveler  should  be  rapid  with  his  level  as  well  as  with  fig- 
Tires.  He  should  calculate  elevations  as  fast  as  the  rod  read- 
ings are  taken  and  should  systematically  check  up  the 
turning  point  and  instrument  heights  as  the  work  proceeds. 
As  results  are  verified  the  same  should  be  indicated  by  check 
marks.  Each  page  of  notes  should  be  checked  by  summing 
up  turning  point  back  and  fore  sight  rod  readings,  and  com- 
paring their  difference  with  the  difference  between  the  first 
and  last  elevations  or  instrument  heights,  as  the  case  may 
be,  on  the  page.  Follow  the  prescribed  form.  As  far  as 
possible,  bench  marks  should  be  checked  by  including  them 
in  the  circuit  as  turning  points.  Balance  back  and  fore 
sight  distances  on  turning  points.  Permanent  bench  marks 
should  be  established  at  least  every  1500  feet,  and  located 
in  places  at  once  convenient  and  free  from  disturbance 


LEVEL  PARTY. 


177 


during  construction.  Later  levels  should  check  within  0.05 
foot  into  the  square  root  of  the  length  of  circuit  in 
miles.  When  a  discrepancy  is  found,  a  line  of  check  levels 
must  be  run  to  fix  responsibility  for  the  error.  In  cross- 
ing streams,  secure  high  water  elevations,  with  dates,  es- 
pecially of  extraordinary  Hoods,  also  low  water  level.  In 
crossing  highways  obtain  elevations  each  side  for  some 
distance  with  a  view  to  avoid  grade  crossings.  In  going  up 
or  down  steep  slopes,  gain  all  the  vertical  distance  possible 
each  setting,  and  follow  a  zig-zag  course.  The  bottom  of 
deep  gullies  may  be  determined  by  hand  level.  Assist  the 
rodman  in  plumbing  the  rod,  and  on  turning  points  and 
benches  have  the  rod  gently  swung  in  a  vertical  plane  to  and 
from  the  instrument  and  take  the  minimum  reading.  The 
self-reading  rod  is  to  be  preferred.  Many  levelers  use  the 
Philadelphia  rod  without  target.  If  the  target  is  used  on 
turning  points,  the  leveler  should  check  the  rod  reading 
when  practicable. 

Completeness,  correctness  and  neatness  of  notes  and  rec- 
ords, and  facility  and  accuracy  in  'handling  the  level  will 
be  given  chief  weight  in  fixing  the  merit  of  the  leveler's 


178  RAILROAD  SURVEYING. 

work.  The  level  notes  are  to  be  returned  at  the  end  of  the 
day's  work. 

Rodman.— (Leveling  rod,  peg  book,  hatchet,  turning 
point  pegs,  spikes,  keel.)  The  rodman  holds  the  rod  at 
station  stakes  and  at  such  plus  points  as  may  be  required 
to  make  a  representative  profile.  It  is  his  duty  to  identify 
each  station  point  and  be  on  the  lookout  for  duplicated  or 
omitted  stations.  To  this  end  he  should  habitually  pace  in 
each  station,  especially  in  grass  or  underbrush,  and  call  out 
or  signal  the  station  number  to  the  leveler.  Should  a  blunder 
in  station  numbering  appear,  he  should  positively  confirm 
the  fact  by  retracing  several  stations,  and  then  carry  the 
corrected  stationing  ahead.  The  rod  should  be  held  truly 
plumb,  which  is  best  done  by  standing  squarely  behind  the 
rod  and  supporting  it  with  the  tips  of  the  fingers  of  both 
hands.  On  turning  points,  the  rod  should  be  waved  gently 
in  a  vertical  plane  to  and  from  the  instrument.  The  rod- 
man should  pay  special  attention  to  placing  the  target 
right  for  long  rode  and  examine  it  to  note  if  it  has  slipoed 
before  reading  the  rod.  Errors  of  1  foot.  0.1  foot.  etc.. 
should  be  carefully  guarded  against.  Turning  noints  should 
be  selected  with  special  reference  to  their  solidity,  and  care 
should  be  taken  not  to  disturb  them.  Station  pegs  and 
hubs  are  often  used  for  turning  points:  when  so  xised,  the 
precise  fore  sight  to  0.01  foot  should  follow  the  usual  ground 
rod  reading  to  the  nearest  0.1  foot.  The  rodman  should 
use  good  judgment  in  selecting  bench  marks,  locating  them 
out  of  reach  of  probable  disturbance  during  construction 
and  describing  them  so  as  to  be  easily  found.  He  should 
be  active  and  do  his  best  to  keep  close  up  with  the  transit 
party.  The  rodman  should  keep  a  peg  book  for  recording 
turning  points  and  instrument  heights,  and  check  his  com- 
putations independently  and  compare  results  with  the 
leveler. 

TOPOGRAPHY  PARTY.— It  is  the  purple  of  the 
topography  party  to  secure  full  data  for  manning  contours, 
property  lines,  buildings,  roads,  streams,  and  other  import- 
ant topographic  details.  The  width  of  territory  to  be  em- 
braced in  the  survey  depends  on  local  conditions:  in  places 
it  may  be  as  much  as  one-fourth  or  one-half  mile  from  the 
line,  although  it  is  usually  better  to  run  alternate  lines  when 
the  distance  to  be  included  becomes  so  great.  The  topog- 


TOPOGRAPHY  PARTY.  179 

raphy  party  often  consists  of  only  two  men,  but  a  party 
of  four  is  much  more  efficient.  Sometimes  no  regular  topog- 
raphy party  is  provided,  but  after  running  a  few  miles  of 
line  ahead,  the  transit  and  level  parties  are  formed  into 
several  parties  to  bring  the  topography  up  to  the  end  of  the 
preliminary  line.  For  student  practice  the  topography 
party  will  consist  of  four  members:  (1)  topographer,  (2) 
assistant  topographer,  (3)  topography  rodman,  (4)  tapeman. 

Topographer. —  (Topography  board,  topography  sheet  (or 
several  sheets),  hard  pencil,  compasses,  eraser,  etc.)  The 
topography  sheet  should  be  prepared  before  going  to  the 
field,  showing  the  alinement  and  other  data  needed  from  the 
transit  notes.,  and  elevations  of  all  stations  and  pluses  from 
the  level  notes.  Cross-section  paper  is  to  be  preferred. 
The  center  line  may  be  plotted  to  one  side  of  the  center  line 
of  the  sheet,  when  the  topography  is  to  be  takf-n  farther  in 
one  direction  than  the  other.  In  order  to  secure  full  details, 
the  scale  of  the  field  plat  may  well  be  double  (or  even  more) 
that  of  the  finished  map.  The  topography  sheet  should  show 
local  conditions,  such  as  gravel  banks,  rock  ledges,  etc., 
suitable  for  ballast  or  other  constructive  use;  out-croopings 
of  rock  or  other  material  which  may  affect  the  classification 
of  the  graduation;  character  of  substrata  at  sites  of  bridge 
or  other  masonry  work;  springs,  wells,  streams,  etc.,  suit- 
able for  water  supply;  approximate  flood  levels  and  other 
data  relating  to  waterways  or  surface  drainage;  location  of 
streams,  especially  with  reference  to  desirable  crossings, 
freedom  from  probable  change  of  channel,  etc.;  location  of 
highways  including  elevations  some  distance  either  way 
with  special  reference  to  avoiding  grade  crossings;  other 
railroad  lines,  with  the  same  point  in  view;  character  and 
condition  of  crops  and  other  farm  improvements,  names  of 
ov.-ners,  etc.. — in  short,  any  and  all  information  that  is  at  all 
likely  to  be  of  service  in  mapping  the  route,  projecting  the 
location,  during  construction,  etc.  In  locating  a  group  of 
buildings  some  distance  from  the  line,  fix  the  principal  one 
by  tie  lines,  by  intersection  or  polar  coordinates,  and  the 
others  by  measurement  and  sketch  from  it.  Locate  build- 
ings near  the  line  by  rectangular  offsets,  or  by  intersections 
of  the  principal  outlines  with  the  survey  line.  Contours  are 
located  by  means  of  the  hand  level  used  by  the  assistant 
topographer.  The  contour  interval  should  be  five  feet  or- 


180  RAILROAD  SURVEYING. 

dinarily,  but  may  be  increased  to  ten  or  more  feet  on  very 
steep  slopes.  The  contour  data  should  be  selected  with 
special  reference  to  ridge  and  gully  lines  (see  problem  and 
plat  on  contour  leveling,  Chapter  IV.)  Ordinarily  hand 
level  lines  may  be  run  out  at  right  angles;  angling  lines 
along  gulches  and  ridges  may  be  located  by  estimation, 
pocket  compass  or  tie  lines.  The  plat  is  made  by  the  topog- 
rapher from  data  collected  by  the  other  members  of  the 
party.  A  common  fault  with  the  beginner  in  such  work  is 
the  omission  from  the  plat  of  important  numerical  data, 
such  as  station  numbers  of  land-line  crossings,  etc.,  owing 
to  an  undue  attention  to  the  minute  details  of  the  drafting 
work.  A  good  topography  record  with  contour  notes'  on 
the  left  hand  page  and  field  sketch  showing  all  numerical 
data  on  the  right,  is  shown  in  the  accompany  form. 

Assistant  Topographer. —  (Hand  level,  pocket  compass, 
topography  note  book.)  It  is  the  duty  of  the  assistant 
topographer  to  collect  data  for  the  use  of  the  topographer 
in  making  the  plat.  He  uses  the  hand  level,  notes>  station 
numbers,  distances,  bearings,  etc.,  and  makes  such  record 
of  the  same  as  may  be  required  to  fit  local  conditions.  In 
COP  touring,  a  special  rod  with  adjustable  base  (see  Fig.  19, 
Chapter  IV.),  if  available,  may  be  used;  otherwis-e,  an  or- 
dinary flag  pole  with  alternate  feet  red  and  white  is  em- 
ployed. Beginning  with  the  known  profile  elevation,  as  ex- 
tracted from  the  leveler's  record,  even  five-foot  contours  are 
located,  as  a  rule,  nominally  every  200  to  500  feet  at  right 
angles  to  the  line,  except  as  ruling  ridges  or  gullies  may 
suggest  other  directions.  His  record  should  be  ample  and 
legible,  and  include  data  and  information  which  may  not 
properly  be  placed  on  the  plat.  All  estimated  elevations, 
distances  or  dimensions  should  be  noted  as  such.  The  assist- 
ant topographer  works  under  the  direction  of  the  topog- 
rapher, but  is  expected  to  take  the  initiative  in  the  collec- 
tion of  data  so  as  to  permit  his  superior  to  devote  proper 
attention  to  the  field  plat. 

Topography  Rodman.— (Topography  rod  with  adjust- 
able base  (see  (f),  Fig.  19,  Chapter  IV.)  or  flag  pole,  hatchet.) 
It  is  the  duty  of  the  rodman  to  hold  the  topography  rod  as 
directed  by  the  assistant  topographer.  He  should  be  active 
and  continually  on  the  alert  for  information  or  data  which 
the  record  book  or  sheet  should  contain.  The  rodman  holds 


OFFICE  WORK. 


181 


the  zero  end  of  the  tape  in  measuring  the  distances.  He 
should  acquire  skill  in  pacing  on  rough  as  well  as  smooth 
ground,  and  when  sufficiently  exact  especially  on  ground 
remote  from  the  surveyed  line,  he  should  gain  time  by  pac- 
ing in  the  distances  to  contour  lines. 

Tapeman. — (Metallic  (or  band)  tape,  set  of  chaining  pins, 
flag  pole.)  It  is  the  duty  of  the  tape-man  to  determine  dis- 
tances with  the  help  of  the  rodman.  He  should  be  vigilant 
in  checking  up  tallies,  reading  fractions,  leveling  the  tape, 
breaking  chain,  plumbing  down  ends,  etc.,  and  should  never 
be  the  cause  of  needless  delay  in  the  work.  When  required, 
he  should  measure  angles,  take  tie  lines,  etc.,  with  the  tape. 

OFFICE  WORK. — The  office  work  of  each  student  in- 
cludes; (1)  reconnaissance  map,  profile  and  report;  (2)  map 
showing  preliminary  lines  with  topography  and  projected 
location  lines;  (3)  preliminary  profile  with  grade  lines,  ap- 
proximate estimate  of  quantities,  etc.;  (4)  final  location  map 
(traced  from  preliminary  map) ;  (5)  location  profile;  (6) 
copies  of  field  notes;  (7)  cross-section  notes  and  estimate 
of  graduation  quantities;  (8)  estimate  of  cost  of  construc- 
tion; (9)  monthly  estimates,  progress  profile,  haul,  pris- 


182  RAILROAD  SURVEYING. 

moidal  and  curvature  corrections,  vouchers,  etc.,  final 
estimate. 

Reconnaissance  Report. — The  reconnaissance  map 
showing  the  area  examined  will  be  based  upon  such  maps 
of  the  route  as  may  be  available.  It  should  show  the  sev- 
eral ruling  points  and  general  routes  selected  for  actual 
survey.  The  profile  should  be  based  upon  barometric  or 
hand  level  observations  and  distances  scaled  from  the  map 
or  determined  roughly  by  pacing  or  otherwise  on  the 
ground.  The  report  should  refer  to  the  map  and  profile 
and  state  the  general  scheme,  the  several  ruling  considera- 
tions or  conditions,  the  details  of  the  examination,  a  rough 
comparison  of  the  several  alternative  routes,  and  a  final 
summary  and  conclusion  with  definite  recommendations. 
The  report  should  be  made  in  accordance  with  best  usage  as 
to  form,  composition,  etc. 

(Considering  the  limited  point  of  view  of  the  beginner, 
the  reconnaissance  reports  may  not  be  required  until  the 
actual  surveys  are  well  along.  In  such  case,  however,  the 
student  is  not  to  draw  data  from  sources  other  than  those 
above  outlined.) 

Preliminary  Map. — Themappingshould  be  the  best  prod- 
uct of  the  student's  skill  as  a  draftsman,  and  should  con- 
form closely  to  the  department  standards,  which  are  based 
upon  best  current  usage  of  leading  American  railroads.  Un- 
less otherwise  instructed,  the  preliminary  map  will  be  made 
on  eggshell  or  paragon  paper.  There  are  three  ways  to  plot 
the  skeleton  of  the  preliminary  survey:  (1)  by  laying  off 
each  successive  deflection  angle  and  distance  from  the  pre- 
ceding line;  (2)  by  laying  off  the  successive  calculated 
courses  and  distances  from  a  precisely  drawn  meridian  or 
other  reference  line;  and  (3)  by  rectangular  coordinates. 
The  first  method  should  not  be  used,  since  cumulative  errors 
are  probable.  The  second  is  rapid  and  free  from  serious 
objection;  if  preferred,  a  modified  base  line  may  be  assumed 
and  the  calculated  bearings  transferred  to  the  same;  the 
angles  may  be  laid  off  by  means  of  scale  and  table  of  nat- 
ural trigonometric  functions  from  a  precisely  drawn  base 
line  and  then  transferred,  as  required,  by  parallel  ruler  or 
triangle;  this  method  is  used  most  in  practice.  The  third 
method  is  the  most  exact,  and  will  be  used  by  the  student 
unless  the  second  is  specified.  It  involves  the  calculation  of 


OFFICE  WORK. 


183 


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184  RAILROAD  SURVEYING. 

a  plotting  sheet,  as  shown  in  the  accompanying  form.  The 
axis  is  usually  a  meridian  line,  but  any  line  may  be  taken 
and  the  courses  changed  to  suit.  In  making  the  plotting 
table,  the  data,  calculated  bearings,  distances,  etc.,  should 
be  carefully  checked  through  to  the  last  point  in  the  skele- 
ton before  the  plotting  is  begun.  Only  one  axis  should  be 
plotted,  preferably  the  one  having  greater  totals,  so  as  to 
give  short  perpendiculars.  Starting  from  the  origin,  1000- 
foot  points  are  pricked  in  along  the  axis  to  the  specified 
scale,  and  marked  0,  10,  20,  etc.;  the  totals  are  interpolated 
on  the  axis  and  lettered;  exact  perpendiculars  about  the 
right  length  are  erected;  the  second  point  is  established  by 
scaling  the  perpendicular  and  the  line  is  checked  back  on 
the  preceding  point;  if  correct,  the  stations  are  pricked  in 
and  every  fifth  station  and  deflection  points  are  enclosed  in 
a  small  circle  and  neatly  numbered;  the  next  course  is  so 
located  and  checked  back  by  length  of  hypothenuse,  the  sta- 
tions fixed  and  numbered,  and  so  on  to  the  end  of  the  line; 
the  courses  should  be  taken  in  their  order  and  none  passed 
without  checking  satisfactorily.  After  the  skeleton  is  com- 
pleted, the  topographic  details  are  penciled  in,  and  the  map 
finished  and  inked.  The  title,  border,  meridian  (both  true 
and  magnetic),  etc.,  should  be  first-class  in  quality  and  in 
keeping  with  the  rest  of  the  map.  Crude  or  careless  letter- 
ing or  other  details  of  the  map  will  cause  its  rejection.  The 
title  of  the  map,  profile,  etc.,  should  be  given  in  brief  on  the 
outside  of  the  sheet  or  roll  at  each  end. 

Preliminary  Profile. — Use  Plate  A  profile  paper  in  mak- 
ing the  profiles.  The  level  notes  should  first  be  carefully 
verified  and  then  one  person  should  read  off  while  another 
plots  the  data.  A  hard  pencil,  6H  or  7H,  sharpened  to  a 
long  needle  point  should  be  used.  The  stations  are  first 
numbered  along  the  bottom  from  left  to  right  (or  the  re- 
verse, as  prescribed);  leaving  six  inches  or  so  at  the  left  for 
a  title,  and  beginning  at  a  prominent  line  with  station  0, 
every  tenth  station  is  so  numbered.  The  notes  are  examined 
for  lowest  and  highest  elevation  and  a  prominent  line  is 
assumed  as  an  even  50  or  100-foot  value  relative  to  the 
datum.  The  horizontal  scale  is  400  feet  and  the  vertical 
scale  20  feet  to  the  inch.  Points  should  be  plotted  no  heav- 
ier than  necessary,  since  the  surface  of  profile  paper  will 
not  permit  much  erasing.  The  surface  line  should  be  traced 


OFFICE  WORK,  185 

in  close  up  to  the  plotted  points,  owing  to  the  danger  of 
overlooking  abrupt  breaks  such  as  streams,  ditches,  etc. 
Pluses  should  be  fixed  by  estimation.  The  surface  line  when 
completed  should  be  inked  with  a  ruling  pen  used  freehand; 
the  weight  of  the  line  should  be  about  the  average  of  the 
ruled  lines  on  the  profile  paper.  (A  special  profiling  or  con- 
touring pen  is  much  used  for  this  purpose.)  The  profile 
should  show  the  grade  line,  grade  intersection,  elevations 
and  rates  of  grade  in  red;  water  levels,  and  data  relative 
to  same  in  blue;  surface  line,  station  numerals,  etc.,  in 
black;  the  alinement,  important  land  lines,  streams,  etc., 
should  be  shown  at  the  bottom  of  the  profile  in  black.  The 
grade  line  should  be  laid  nominally  with  a  view  to  balance 
the  cut  and  fill  quantities,  but  this  should  be  varied  to 
suit  local  conditions,  such  as  drainage,  the  elimina- 
tion of  grade  crossings,  classification  of  materials,  etc.  The 
maximum  gradients,  the  rate  of  compensation  for  curva- 
ture, etc.,  will  be  made  to  suit  the  specified  conditions.  The 
compensation  for  curvature  will  be  allowed  for  on  the  pre- 
liminary profile  by  dropping  the  grade  line  on  maximum 
gradients  at  each  deflection  point.  Grade  intersection  ele- 
vations and  rates  of  grade  will  be  given  to  the  nearest  0.01 
foot. 

Approximate  Estimates. — Rapid  estimates  of  earth- 
work quantities  may  be  made  direct  from  the  profile  either 
by  reference  to  a  table  of  level  sections,  or  preferably  by 
means  of  an  earthwork  scale,  shown  in  the  accompanying 
diagram.  This  scale  is  graduated  in  hundreds  of  cubic 
yards  for  the  particular  roadbed  base  and  side  slopes.  The 
data  for  making  the  scales  are  given  in  the  table.  The 
quantities  may  be  jotted  down  for  addition  or  lumped  men- 
tally, or  an  adding  strip  may  be  inserted  in  slits  near  one 
edge  of  the  scale.  In  using  this  scale  it  is  customary  to 
make  no  deduction  for  minor  waterways.  Estimates  made 
in  this  way  from  the  profile  of  a  careful  preliminary  survey, 
often  do  not  vary  more  than  five  per  cent  from  the  final 
construction  quantities. 

Location  Map. — The  location  map  may  be  traced  from 
the  preliminary  map  and  should  include  the  topography  and 
such  details  as  usually  appear  on  the  final  record  map  of  the 
located  line.  Contour  lines  may  be  traced  in  cadmium  yel- 
low to  insure  satisfactory  blue  printing. 

Location  Profile. — The  location  profile  should  be  exe- 


186 


RAILROAD  SURVEYING. 


14-FT.  ROADBED. 
SLOPES  1£  To  I. 

Hundred  of  Cu.Yds. 
per    Station. 


20-Fr.  ROADBED. 
SLOPES  1  To  I. 


96   — 


Fig.  39. 

cuted  according  to  the  standard  specimen,  and  should  in- 
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tual cross-section  notes,  and  quantities  of  other  construc- 
tion materials.  Curvature  compensation  will  be  shown  on 
the  location  profile  by  reduced  maximum  gradients.  Verti- 
cal curves  will  be  calculated  at  a  rate  of  change  not  to  ex- 
ceed 0.05  foot  per  station,  except  at  summits  where  it  may 
be  0.10  foot  or  more  per  station.  It  should  be  prepared  as 


OFFICE  WORK. 


187 


CENTER  CUT  OR  FILL.  IN  FEET 

FOR  GIVEN  QUANTITIES   PER  STATION. 

(DATA  FOR  EARTHWORK  SCALE.) 


CUBIC 
YARDS 
Per 

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SIDE  SLOPE,  I  TO  1. 

SlDESLOPE.ll  TO  I. 

CUBIC 
YARDS 
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100 
Feet 

WIDTH  OF  ROADBED 
in  Feet. 

WIDTH  OF  ROADBED 
in  Feet. 

Feet 

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20 

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188  RAILROAD  SURVEYING. 

the  final  record  profile.  Approximate  profiles  of  projected 
lines,  determined  from  the  contour  map,  with  rough  esti- 
mates of  quantities  will  also  be  prepared,  as  specified. 

Office  Copies  of  Notes. — The  complete  level  and  transit 
notes,  and  topography  notes  as  assigned,  must  be  copied 
in  the  individual  books  by  each  student.  These  copies  will 
be  in  pencil  (or  ink  if  so  specified)  and  will  be  executed  in 
a  faithful  and  draftsmanlike  manner  according  to  the  de- 
partment standards  of  lettering,  etc. 

Estimates  of  Quantities.— The  cross-section  notes  will 
be  copied  and  the  quantities  of  excavation  and  embankment 
calculated,  as  assigned.  The  cross-sectional  areas  will  be 
calculated  arithmetically  and  checked,  especially  on  rough 
ground,  by  means  of  planimeter.  The  quantities  will  be 
calculated  by  average  end  areas,  by  tables,  and  by  diagrams, 
so  as  to  afford  ample  practice  for  the  student  in  all  the  cur- 
rent methods.  The  estimate  will  also  include  all  the  other 
materials  of  construction. 

Estimate  of  Cost. —  Each  student  will  make  a  detailed 
summary  of  the  quantities,  fix  prices,  and  estimate  the 
probable  total  cost  of  the  work,  or  of  the  assigned  section. 
The  prescribed  form  will  be  followed.  The  prices  should 
be  based  on  local  conditions  as  far  as  possible. 

Construction  Estimates. — Monthly  estimates,  estimates 
of  haul,  borrow  pit  estimates,  classification,  prismpidal  and 
curvature  corrections,  progress  profile,  vouchers,  force  ac- 
count, etc.,  and  final  estimate  will  be  prepared  by  each 
student  in  accordance  with  prescribed  forms  and  standards. 

Right  of  Way  Records. — Each  student  will  be  assigned 
a  share  of  work  in  the  preparation  of  right  of  way  deeds 
and  record  maps.  The  following  forms  (from  the  ''Engi- 
neering Rules  and  Instructions,"  Northern  Pacific  R.  R.) 
will  be  used  as  models  in  preparing  right  of  way  descrip- 
tions. 

(Through  government  subdivisions):  "A  strip,  piece  or 
parcel  of  land  one  hundred  feet  in  width,  situated  in  the 
northwest  quarter  of  the  northwest  quarter  of  section  ten, 
in  township  two  north,  range  one  west  (S.  10,  T.  2  N.,  R. 
1  W.),  Madison  county,  Montana,  and  having  for  its  bound- 
aries two  lines  that  are  parallel  with  and  equidistant  from 
the  center  line  of  the  railroad  of  the  —  —  Railway  Com- 
pany, as  the  same  is  now  located  (and  constructed.)  For  a 


CROSS-SECTIONING. 


189 


(ESTIMATE      OF    COST     OF 

RAILROAD    c 

OMSTR 

JCTION.) 

ITEM. 

M<,«ur<! 

Price 

Quantity 

An,*.*. 

/.  Carth  Excavation. 

Cu.  You, 

Z.  forth  Embankment  Sorrowed. 

CV.  Yds. 

3  Earth  Embankment  Ovrrnat/f*ot. 

CuYd-Stas. 

4.  Loose  ftoctl  Excavaf/ort. 

Cu.  Ya/s. 

Sotiet  ffocft  Excavation. 

Cu  Yo/e. 

Clearing. 

Acres. 

Grubbing. 

Sta. 

BRIO      NO,  CULVERTS.  ETC. 

Timber  in  Bridges. 

M.Ft  B.H. 

Iron  in  Bridge*. 

Lbs. 

Pi/ing  Driven. 

Lin.  Ft. 

Timber  in  Culvert*. 

M.F*  B.M. 

Iron  in  Cu/vrrts. 

Lit. 

Vitrified  />/>». 

iia.ff. 

Caffle  Suordf. 

Cach. 

L  umber  in  ffoad  Cros  f,ings. 

M.Ft.  8  M. 

Sfifm  in  Crosses. 

Lbs. 

TRA      . 

Ties. 

EorcA. 

Rail.fWf.prrvd.) 

LongTont. 

An9lfB<trs.(m  pn-  pair) 

Lbs. 

Tracn-Bo/n.  (Stir.) 

Htas^.pr.Kg) 

S/oities.fSiie.) 

Hfgs(Wf.fr.H3. 

3~itch  Stands  and  Fixtures. 

Sett. 

frogs. 

Each. 

$*fifch   Timbers. 

Sets. 

TKM:*  Laying   and  Surfact'ng. 

Miles. 

MIS       LLANEOU&. 

Fenc/no. 

fleets. 

Tf/ear<*ph  Line, 

flUes. 

Builctinas. 

Each. 

"'•9**  of  Way. 

AerfS. 

f*r  Cent. 

more  particular  description,  reference  may  be  had  to  the 
plat  drawn  upon  and  made  a  part  of  this  deed." 

(Lots  in  platted  tracts):  "Lot  seven  (7),  block  six  (6),  in 
Smith's  addition  to  Helena,  Lewis  and  Clark  county, 
Montana,  according  to  the  recorded  plat  thereof." 

CROSS-SECTIONING  PARTY.— It  is  the  duty  of  the 
cross-sectioning  party  to  set  slope  stakes  for  the  proposed 
roadbed  and  to  secure  data  for  the  calculation  of  earth- 
work quantities.  The  data  should  first  be  transcribed  from 
the  location  level  notes  and  profile  into  the  cross-section 
book,  including  station  numbers,  surface  and  grad«e  eleva- 
tions, rates  of  grade,  bench  mark  record,  etc.  In  order  to 
avoid  confusion  in  relation  to  directions  right  and  left,  the 
station  numbers  should  run  up  the  .page,  and  plenty  of 
space  left  for  pluses  in  the  notes,  especially  on  rough 


190 


RAILROAD  SURVEYING. 


FOR^ 

FOR 

ROSS- 

SCCTIOM 

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Surf  Rod 

Grodettofl 

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U 

c 

R 

Perr,CTr«S. 

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7*2.5 
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720.S 

7V.C 

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-8.3 

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, 

iza 

720.1 

73e.SH 

S  .1 

CA<./»«J 

Bridge  Ho.  fS$lZB  +34 

r«K* 

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Sf 

ff<S3» 

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r^«° 

(Toelf^pl^0 

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f 

fSO 

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fl3 

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«7 

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736  50 

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13.0 

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tS2 

(Level  Section  m  cu+.) 

fSt 

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7.3 

/3.0 

B.M.NOIZ 

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f-S.7 

(4-ter*/  section  m  cot; 

** 

746.  1 

mo. 

3.4 

13.0 

^^ 

«» 

+36 

"^ 

{sc^e2o^'frnco"} 

TYPICAL  CASES 


CROSS-SECTIONING 


191 


130 


129 


HEAD     OF    DUMP. 


+54 


CROSS-SECTION      AT      STATION      125. 

ECvfT 


IE5 


192  RAILROAD  SURVEYING. 

ground.  As  shown  in  the  form,  the  left  hand  page  sho-ilcl 
be  used  for  data  and  the  other  for  the  cross-section  notes. 
The  organization  and  equipment  of  the  cross-sectioning 
party  when  using  the  engineers'  level  is:  (1)  recorder 
(notebook),  (2)  leveler  (engineer's  level),  (3)  rodman  (self- 
reading  leveling  rod,  50-foot  tape),  (4)  axeman  (axe,  sack  of 
flat  stakes,  marking  keel).  The  usual  routine  is:  (1)  De- 
termine height  of  instrument  by  back  sight  on  identified 
bench  or  turning  point.  (When  a  bench  mark  is  remote 
and  an  original  turning  point  can  not  be  found,  it  may 
suffice  in  an  emergency  to  check  on  the  ground  at  several 
stations  to  the  nearest  0.1  foot  and  use  the  mean  height  of 
instrument.  Such  places  should  be  verified  later.)  (2) 
Having  the  height  of  instrument,  check  the  original  eleva- 
tion of  the  station  about  to  be  cross-sectioned,  reading  the 
rod  and  checking  off  the  elevation  if  it  does  not  differ  more 
than  0.1  foot  or  so;  in  case  of  a  new  plus,  take  a  rod  read- 
ing and  record  the  elevation.  (3)  Determine  the  "grade 
rod"  for  the  station  by  subtracting  the  height  of  instrument 
from  the  grade  elevation;  then  note  that  cut  or  fill  at  any 
point  of  the  cross-section  is  equal  to  surface  rod  minus 
grade  rod;  (counting  rods  as  minus  when  downward  from 
the  plane  of  the  level  and  those  upward  as  plus,  this  rule 
gives  results  always  plus  for  cut  and  minus  for  fill,  which 
agrees  with  the  conception  that  cross-section  notes  are 
rectangular  coordinates  of  the  sectional  area  referred  to 
the  center  of  the  finished  roadbed  as  an  origin.)  (4)  If  the 
ground  is  level  transversely,  that  is.  does  not  vary  more 
than  0.1  foot  or  so  within  the  limits  of  the  proposed  grad- 
ing, then  the  distance  from  the  center  out  to  each  side 
slope  stake  is  half  width  of  roadbed  plus  center  cut  or  fill 
times  rate  of  side  slope;  (thus  for  20- foot  roadbed,  side 
slopes  1  to  1,  and  a  cut  of  18.6  feet,  the  distance  out  to  slope 
stake  on  a  level  section  would  be  28.6  feet,  or  with  a  =lon>3 
of  1%  to  1,  the  distance  out  would  be  10  plus  l1^  times  18.6. 
or  37.9  feet.  Calculations  of  this  sort  should  be  dope  men- 
tally in  an  instant.)  (5)  On  three-level  ground  estimate 
the  rise  or  fall  of  the  surface  from  the  center  to  about 
where  the  side  slope  stake  should  come,  and  add  the  same 
to,  or  subtract  it  from  the  center  cut  or  fill,  as  U.e  case 
may  be;  compute  the  distance  out  to  the  point  where  the 
side  slope  line  would  pierce  the  ground  surface  and  test 


CROSS-SECTIONING.  193 

the  same  with  tape,  rod  and  level  by  the  foregoing  rule  for 
cut  or  fill;  continue  to  construct  points  on  the  side  slope 
line  until  the  common  point  is  found.  (6)  The  axeman 
marks  "S.  S."  (slope  stake)  on  one  side  of  the  stake  with 
the  cut  or  fill  to  the  nearest  0.1  foot  (as  C  6.8  or  F  10.2)  and 
the  station  number  on  the  other  side;  the  stake  is  driven 
slanting  towards  or  away  from  the  center  line  according 
as  it  is  cut  or  fill.  (7)  On  five-level  ground  or,  in  general, 
on  ground  involving  any  number  of  points  or  angles  in  the 
section,  the  cut  or  fill  is  taken  at  each  break.  (8)  Should 
there  appear  to  be  danger  of  land  slips,  the  cross-sectioning 
should  be  carried  well  beyond  the  limits  of  the  slops  sta\e 
points.  (9)  The  cross-section  notes  are  recorded  as  in  the 
accompanying  form,  expressing  the  coordinates  of  each 
point  in  the  form  of  a  fraction,  and  distinguishing  the  slope 
stake  points  by  enclosure  in  a  circle.  (10)  Having  com- 
pleted the  cross-sectioning  at  the  station,  the  same  program 
is  followed  at  the  next  point,  first  checking  the  elevation 
obtained  in  the  original  location  levels;  the  jjrad^  rod 
should  be  determined  as  before  by  subtracting  the  height 
of  instrument  from  the  grade  elevation,  and  Chen  checked 
by  applying  to  the  preceding  grade  rod  the  rise  or  fall  of 
grade  from  the  preceding  point.  (11)  Cross-sections  should 
be  taken  as  a  general  rule  at  every  station  and  at  ?ueh 
intermediate  points  as  will  insure  a  reliable  measurement 
of  the  earthwork  quantities.  It  is  not  necessarily  the  low- 
est and  highest  points  that  are  required,  but  those  points 
which,  when  joined  by  straight  lines,  will  give  the  contents 
as  nearly  as  possible  equal  to  the  true  volume;  if  the  "aver- 
age end  areas"  method  is  to  be  used  in  calculating  the  Quan- 
tities, sections  should  be  taken  every  50  feet  when  the  dif- 
ference of  center  height  is  as  much  as  5  feet;  as  a  rule, 
slope  stakes  need  not  be  set  at  cross-sections  taken  between 
stations.  (12)  "Grade  point"  stakes  (marked  0.0),  should 
be  set  where  the  center  line  and  each  edge  of  the  roadbed 
pierce  the  ground;  and  also  in  side-till  sections  in  both  cut 
and  fill,  where  the  roadbed  plane  cuts  the  ground  line;  if 
the  width  of  roadbed  is  different  in  cut  and  fill,  the  greater 
half-width  is  commonly  used  in  locating  the  side  grade 
point;  in  the  simplest  case  a  contour  line  is  perpendicular 
to  the  center  line  and  the  three  grade  points  are  at  the 
same  cross-section,  forming  two  wedges;  in  the  more  usual 


194  RAILROAD  SURVEYING. 

case  the  contour  line  is  diagonal,  and  the  three  grade 
points  are  not  in  the  same  section,  so  that  two  pyramids  are 
formed;  if  the  station  numbers  of  the  two  side  grade  points 
differ  by  only  a  few  feet,  it  is  usual  to  simplify  the  record 
by  taking  the  notes  as  for  a  wedge  at  the  station  uumber  of 
the  center  grade  point,  although  the  side  grade  point  stakes 
are  set  in  their  true  positions;  as  a  rule,  a  complete  cross- 
section  is  taken  at  each  grade  point.  (13)  In  cross-section- 
ing for  the  end  of  an  embankment  at  a  wooden  trestle  the 
end  slope  is  made  the  same  as  the  side  slope,  and  the  end 
and  side  planes  are  joined  by  conical  quadrants;  the  dis- 
tance between  "heads  of  dump"  (H.  D.)  is  usually  10  feet  (5 
feet  at  each  end)  less  than  the  total  length  of  stringers;  a 
complete  cross-section  is  taken  at  the  "head  of  dump,"  and 
the  "toe  of  dump"  (T.  D.)  on  each  edge  of  the  end  slope  is 
located  and  recorded;  on  level  ground  the  volume  of  the 
wedge-like  solid  so  formed  is  found  by  dividing  it  into  a 
triangular  prism  and  two  right  conical  quadrants;  on 
ground  sloping  transversely  the  end  of  dump  is  made  up 
of  a  middle  prismoid  and  two  conical  quadrants,  each  of  the 
latter  being  generated  by  a  variable  triangle  revolved  about 
a  vertical  axis  through  a  corner  of  the  top  roadbed  plane 
at  "head  of  dump." 

The  calculations  in  the  foregoing  method  of  cross-section- 
ing may  be  simplified  by  preparing  a  table  of  distances  out 
for  the  standard  roadbed  widths  and  slopes,  or  by  using  a 
special  tape  having  the  zero  graduation  at  a  distance  from 
the  end  equal  to  the  half-width  of  roadbed,  and  the  re- 
maining graduations  modified  to  suit  the  side  slope  ratio. 
The  calculations  may  be  further  simplified  by  using  a  spe- 
cial rod  havig  an  endless  sliding  tape  graduation.  The  stu- 
dent will  be  given  practice  with  these  labor  saving  devices 
after  he  has  first  acquired  familiarity  with  the  principles 
of  cross-sectioning  without  these  aids. 

Cross-sectioning  with  rods  alone  is  done  in  much  the 
same  manner  as  that  described  above.  Two  rods  aro  used. 
The  usual  length  of  the  rods  is  ten  feet,  and  each  is  gradu- 
ated to  tenths  and  has  a  bubble  vial  in  one  or  both  ends. 
The  slope  stake  point  is  determined  by  leveling  out  from 
the  ground  at  the  center  stake  with  reference  to  the  center 
cut  or  fill,  each  rod  being  held  alternately  level  and  plumb. 
Other  points  in  the  cross-section,  as  well  as  grade  points, 


CROSS-SECTIONING.  195 

etc.,  are  determined  in  the  same  manner.  The  notes  are 
kept  as  in  the  other  method.  On  very  rough  ground,  the 
rod  method  is  usually  the  more  rapid.  Some  engineers 
cross-section  on  rough  ground  by  taking  the  elevation  of 
each  point  and  plotting  the  notes  on  cross-section  paper, 
then  using  the  planimeter  to  determine  the  areas.  Borrow 
pits  are  often  cross-sectioned  by  taking  elevations  at  the 
intersections  of  two  series  of  parallel  lines  forming 
squares. 

Land-Line  Party.— It  is  the  duty  of  the  right  of  way 
party  to  secure  data  for  the  preparation  of  right  of  way 
deeds.  The  party  should  consist  of  at  least  four:  (1)  re- 
corder, (2)  transitman.  (3)  head  chainman,  (4)  rear  chain- 
man,  (the  chainmen  also  to  serve  as  axemen  and  flagmen 
as  required.)  Their  equipment  is  the  usnal  one  of  a  transit 
party  for  such  work.  The  party  should  secure  ties  with 
all  section  and  other  land  lines  whenever  crossed.  The 
notes  should  show  station  numbers  and  angles:  of  intersec- 
tion and  distance  along  land  line  to  the  nearest  identified 
land  corner  and  also  to  important  fences.  As  a  rule,  make 
the  intersection  by  running  through  from  one  corner  to  the 
other.  Where  the  line  passes  through  a  town,  tie  the  cen- 
ter line  to  the  plats,  block  lines,  monuments,  etc.  Secure 
any  records  and  make  tracings  of  any  plats,  etc.,  at  the 
recorder's  office,  that  may  be  of  service  in  preparing  deeds. 

Bridge  and  Masonry  Party. — The  bridge  and  masonry 
survey  party  will  determine  drainage  areas  for  culverts  and 
other  waterways,  prospect  for  foundations,  and  stake  oat 
trestles,  masonry  work,  etc.  The  usual  organization  will 
be  four  men:  (1)  recorder  (in  charge),  (2)  transitman  or 
leveler,  (3)  chainman,  rodman,  flagman,  etc.,  (4)  chainman, 
axeman,  flagman,  etc..  as  the  work  assigned  may  demand. 

Resurvey  Party. — The  resurvey  party  will  be  assigned  to 
such  duties  as  the  resurvey  of  yards,  the  collection  of  data 
for  crossing  frogs,  running  centers  on  old  track,  including 
spiraling,  etc.  It  will  usually  be  a  party  of  four. 

Seminary  Work. — The  purpose  of  the  seminary  work  is  • 
(1)  to  give  the  student  a  knowledge  of  the  literature  of  rail- 
way engineering,  and  (2)  to  afford  training  in  the  collection 
and  preservation  of  engineering  information  and  data,  and 
in  the  preparation  of  abstracts  and  reports  of  a  technical 
nature.  The  reading  will  be  done  in  accordance  with  a 


196  RAILROAD  SURVEYING. 

systematic  outline  and  the  notes  will  be  submitted  in  pre- 
scribed form. 

PROBLEMS  IN   RAILROAD   SURVEYING. 

PROBLEM      Gl.      ADJUSTMENTS      OF      LEVEL      AND 
TRANSIT. 

(a)  Equipment. — Engineers'    level    and   transit,    adjusting 
pin. 

(b)  Problem. — Test  the  essential  adjustments   of  the  as- 
signed instruments  and  correct  any  discrepancies  found. 

(c)  Methods. — This  problem   is   designed  to    freshen   the 
student's  knowledge  of  the  adjustments  of  the  instruments, 
as  well  as  to  place  the  equipment  in  condition  for  accurate 
work.     The  adjustments  will  be  made  under  the  personal 
dirtxrtion  of  the  instructor.    The  student  should  attempt  to 
be  speedy  as  well  as  accurate  in  testing  and  making  the  ad- 
justments. 

PROBLEM  G2.     USE  OF  FIELD  EQUIPMENT. 

(a)  Equipment. — Complete  equipment  for  railroad  transit 
and  level  party,  as  specified  in  foregoing  pages. 

<b)  Problem. — Practice  the  detailed  duties  of  each  position 
in  the  transit  and  level  party. 

(c)  Method*.— This  problem  is  designed  as  a  "breaking  in" 
exercise  preparatory  to  engaging  in  the  regular  field  work 
of  railroad  location.  With  the  manual  in  hand  the  duties 
of  each  position  will  be  studied  and  practiced  in  turn. 

For  example,  each  student  will  go  through  the  following 
exercise  with  the  transit  as  briskly  as  possible:  (1)  set 
transit  over  tack  in  hub,  (2)  level  up,  (3)  set  plate  to  zero, 
(4)  reverse  telescope  and  sight  on  back  flag,  (5)  release 
needle,  (6)  plunge  telescope,  (7)  read  and  record  needle  on 
back  line  prolonged,  (8)  sight  at  front  flag  pole,  (9)  read 
and  record  deflection  angle  right  or  left,  (10)  read  and 
record  needle  on  front  line,  (11)  lift  needle,  (12)  plunge 
telescope  and  check  on  back  flag,  (13)  calculate  needle  angle 
and  compare  with  plate  reading,  and  if  checked,  shoulder 
transit;  now  repeat  entire  process  at  the  same  hub,  more 
briskly  than  at  first,  if  practicable,  avoiding  reference  to 


PROBLEMS. 


197 


preceding  record  until  the  full  series  of  steps  is  completed. 
Let  the  student  prepare  a  similar  numbered  program  for 
each  of  the  other  positions  and  practice  the  same  systemati- 
cally. This  series  of  exercises  may  profitably  occupy  two 
or  more  assignments,  since  the  speed  and  quality  of  the 
actual  surveys  to  follow  are  certain  to  be  much  enhanced. 

PROBLEM   G3.      PRELIMINARY    FIELD   CURVE    PRAC- 
TICE. 

(a)  Equipment. — Transit  party  equipment,  as  prescribed  in 
instructions. 


(Rf  suits  fa  0.0/ 


Problem   2. 


IL__B  CzJiso-n'*.  rt.,Tc,ndE. 

^s£\~>tL,    GiveiWo-**'?'  Ream'red  j  rat  By  1-rigo. 

>-.'>.<         '*•          (.R(4'n')  =  l3376S  I  tb)By  ToUt  I' 

\\A  ^          ' 


Indicated    WorK. 


Length  of  Curve.  L  . 


Tangent    Distancg,  T. 
at  T=f?tan£Z 

=    1337.65  XO.S8  066 
=<7?£7/) 


External  Distance.  £. 


Calculatic 


7)  1 
2 


I7)  '4.0739         60.2 


;*gg3Jj 
/  4.  0739 


376S  T,(eo'/6)=  33Z60 
7;t(o'/8')  =  33283 
T,  (6<f/7)  =  332  7.  /S}&833(3) 

293833  776-77 
76-77  3Z8SS        O.k. 


D,ff  due  to  appro*. 
basis  of   method  (b). 


£>  f60''6'}=  89S 


S36SfO         £>  (60''8')=896S  ____ 

,3376          E,C60'i7'j=89S.9S)4.f833 
6688  8S6S7     209.17 


6688 

6 


_  fi_ 
Z09.,S 


O.OZ 


0  *•      Diff.  due  +o  3o 

appro*,  basis  of  mefhoal  fb}. 


198  RAILROAD  SURVEYING. 

(b)  Problem.— Run  out  the  assigned  practice  curves  in  the 
field,  with  the  prescribed  organization  and  conditions. 

(c)  Methods. — The  preliminary  curve  practice  is  designed 
to  give  the  student  a  practical  knowledge  of  the  principles 
of  railroad  curves  and  the  routine  method's  used  in  location 
surveys.     The  several  positions  in  the  field  party  will  be 
filled  in  succession,  and  each  student  is  expected  to  respond 
heartily  to  the  spirit  of  the  practice,  whatever  his  assigned 
duties.     Each  member  of  the  party  should  engage   in  the 
calculations  as  far. as  practicable.     The  report  of  the  field 
work   should    state   the   precision    of   linear   and    angular 
checks.     The  field  practice  will  be  based  in   part  on   the 
indoor  curve  problems. 

PROBLEM  G4.  CURVE  PROBLEMS. 

(a)  Equipment.—  Drafting  instruments,  paper,  etc, 

(b)  Problem. — Solve  the   assigned   problems    in   railroad 
curves  and  submit  results  in  a  neat  and  draftsmanlike  form. 

(c)  Methods.— (I)  Draw  a  plain  figure  to  the  largest  con- 
venient scale.     (2)    State  problem  and  present  data  in  a 
concise  and  systematic  manner.    (3)  show  the  separate  steps 
clearly;  first  state  formulas  in  general  terms,  then  substi- 
tute values  and  give  results;  as  a  rule,  show  actual  calcu- 
lations adjacent  to  the  indicated  work;    habitually  verify 
results  by  an  independent  process;     use     common     sense 
checks  and  contracted  methods  of  calculation;   in  general, 
make  full  use  of  the  opportunity  to  gain  skill  as  a  com- 
puter.    (As  a  rule,  the  nearest  0.1  foot  only  is  required  in, 
field  measurements  on  curve  location,  but  it  is  excellent 
practice,  especially  for  the  beginner,  to  preserve  the  nearest 
0.01  foot  in  the  calculations.) 


CHAPTER  IX. 
ERRORS  OF  SURVEYING. 


Errors. — Errors  of  observations  are  of  three  kinds,  viz., 
(1)  mistakes;  (2)  systematic  errors;  (3)  accidental  errors. 
Systematic  errors  includes  all  errors  for  which  corrections 
can  be  made,  .as  erroneous  length  of  standard,  errors  of 
adjustment,  refraction,  etc.  Accidental  errors  are  those 
which  still  remain  after  mistakes  and  systematic  errors 
have  been  eliminated  from  the  results. 

It  has  been  found  from  experience  that  accidental  errors 
are  not  distributed  at  random  but  follow  mathematical 
laws.  These  laws  are  fundamental  in  the  Theory  of  Least 
Squares  and  are:  (1)  small  errors  are  more  frequent  than  large 
ones;  (2)  positive  and  negative  errors  are  equally  numerous; 
(3)  very  large  errors  do  not  occur. 

Arithmetical  Mean. — The  most  probable  value  of  a 
quantity  obtained  by  direct  measurements  is  the  arith- 
metical mean  of  all  the  determinations  where  the  observa- 
tions are  of  equal  weight,  or  is  the  weighted  mean  where 
the  observations  are  of  unequal  weight. 

Precision  of  Observations.— In  the  adjustment  of  obser- 
vations it  is  often  necessary  to  combine  results  of  different 
degrees  of  precision  or  weight.  It  is  also  desirable  to  have 
some  means  of  comparing  observations  so  that  the  com- 
puter may  know  what  degree  of  confidence  to  place  in  the 
results.  The  quantity  commonly  used  for  comparing  the 
precision  of  observations  is  the  probable  error. 

Probable  Error.—  The  probable  error  is  such  a  quantity 
that  it  is  an  even  wager  that  the  number  of  errors  greater 
is  the  same  as  the  number  of  errors  less  than  the  probable 
error.  It  is  also  the  limit  within  which  the  probability  is 
one-half  that  the  truth  will  fall.  For  example,  if  4.63± 
0.12  is  the  mean  of  a  number  of  observations,  the  true  value 
is  as  likely  to  be  between  4.51  and  4.75  as  it  is  to  be  some 
value  grea'ter  or  less. 

Probable  error  is  also  useful  in  finding  the  relative  weights 
that  should  be  given  different  sets  of  observations,  as  it  has 
been  found  that  the  weights  of  observations  vary  inversely 
as  the  squares  of  their  probable  errors. 


200  ERRORS  OF  SURVEYING. 

Formulas: 

Let  E!  =  probable  error  of  a  single  observation. 

Em  =  probable  error  of  the  mean  of  all  the  observa- 
tions. 

n  =  the  number  of  observations, 
d  =  the  difference  between  any  observation  and  the 
mean  of  all  the  observations. 

S  =  symbol  signifying  sum  of. 
Then  from  the  Theory  of  Least  Squares 

E!  =  0.6745  ^?2  (1) 

Eni  -=  0.6745  J  *  d'  (2) 

1  n(n-l) 

=  =.  (3) 

Vv. 

The  probable  error  of  the  weighted  or  general  mean  is 

Sy^  (4) 

where  2  p  =  summation  of  the  weights. 

The  probable  error  of  a  quantity  with  a  weight  p  is  equal 
to  E0  divided  by  the  square  root  of  p. 

The  probable  error  of  Z  where  Z  =  zx  ±  z2  and  R1?  rt, 

and  r2  are  the  probable  errors  of  Z,  zt  and  z2, respectively,  is 

R?  =  r\  +  r2  (5) 

The  probable  error  of  Z,  where  Z  =  az  is 

R?  =  a2  r2  (6) 

The  probable  error  of  Z,  where  Z  =  zl  z2  is 

R2  =  z2  r2  +  -L\  r?  (7) 

This  would  be  the  probable  error  of  the  area  of  a  rectan- 
gle where  rl  and  r,  are  the  probable  errors  of  the  sides  z, 
and  z2,  respectively. 

Example. — As  an  example  of  the  application  of  these 
formulas  consider  the  two  following  series  of  measurements  of 
an  angle  given  in  Table  I.  The  first  set  was  taken  with  a 
transit  reading  to  10  seconds,  the  second  with  a  transit 
reading  to  30  seconds. 


PROBABLE  ERROR. 


201 


FIRST    TRANSIT. 


SF.COM)    TRANSIT. 


No.  |       Angle. 

d 

d2 

No. 

Angle. 

d 

d' 

O            '              " 

0             '               " 

1 

34     55     35 

2 

4 

1 

34     56     15 

39 

1521 

•2 

35 

2 

4 

2 

55    80 

6 

36 

3 

20 

13 

If.'.i        :; 

54    30 

66 

4356 

4 

05 

28 

784 

4 

55     15 

21 

441 

5 

56     15 

42 

1764 

5             56    00 

24 

576 

6 

55    40 

7 

49 

6 

55     45 

9 

81 

7 

10 

23 

529 

7 

55     30 

6 

36 

8 

30 

3 

9 

8 

55    30 

6 

36 

9 

50 

17 

289 

9 

56    00 

24 

576 

10 

30 

3 

9 

10 

55     45 

9 

81 

Mean  34°  55'  33" 

2cP  =  3610 

Mean  34°  55'  36" 

2cP=-774<> 

Em  =  0. 


7740 


,=  ±6"  .3 


The  weights  of  these  nnan  values  vary  inversely  as  the 
squares  of  the  probable  errors;  or  in  this  case  the  weights 

are  as  -^^  to  g— yj  or  as  12  to  5.  The  most  probable  value 

of  the  angle  measured  with  the  two  transits  will  be  the 
weighted  mean 


17 


=  34°  5-V  33M 


The  probable  error  of  this  result  from  (5)  since 

12  5 

Z  =   17  zi  +  17  z>      is 


ERRORS  OF  SURVEYING. 


12 

Substituting  r22    =  __1  rL  2      we  have 
o 


R!  =  ±  4."3  J..1-2  =  ±  3".6. 
*   17 

For  other  examples  in  the  use  of  probable  error  see  prob- 
able error  of  measuring  a  base  line,  probable  error  of  set- 
ting a  level  target,  probable  error  of  setting  a  nag  pole.  ' 

Angla  Measjrement.  — The  measurement  of  an  angle  re- 
quires two  pointings  and  two  readings.  If  rr  and  rs  are  the 
probable  errors  of  reading  and  pointing,  respectively;  the 
probable  error  of  the  measurement  of  an  angle  will  from  i5| 
be 

R  i  =    l   rr  2  +  rs  2 

If  rt  is  the  probable  error  of  a  single  reading 


If  the  value  of  an  angle  is  determined  by  n  separate  meas- 
urements the  probable  error  due  to  reading  will  be 


If  the  value  of  an  angle  is  determined  b\  measuring  the 
angle  n  times  by  repetition  the  probable  error  due  to  reading 
will  be 


It  will  thus  be  seen  that  the  probable  error  due  to  reading 
is  very  much  reduced  by  measuring  an  angle  by  the  method 
of  repetition.  The  errors  of  pointing,  etc.,  however,  make 
it  doubtful  whether  it  is  ever  advantageous  to  make  n  exceed 
5  or  6  with  an  engineers'  transit. 

Angle  Adjustment. — When  the  three  angles  of  a  triangle 
have  been  measured  with  equal  care  they  should  be  adjusted 


TESTS  OF  PRECISION.  203 

by  applying  one-third  of  the  error  as  a  correction  to  each 
angle. 

When  the  interior  angles  of  a  polygon  having  n  sides 
have  been  measured  with  equal  care  they  should  be  adjusted 
by  applying  one-nth  of  the  error  as  a  correction  to  each 
angle. 

When  n — 1  angles  and  their  sum  angle  at  a  point  have 
been  measured  with  equal  care  they  should  be  adjusted  by 
applying  one-nth  part  of  the  error  as  a  correction  to  each 
angle. 

In  a  quadrilateral  the  true  values  of  the  angles  fulfil  the 
following  geometrical  conditions:  (1)  the  sum  of  the  angles 
of  each  triangle  is  equal  to  180°  plus  the  spherical  excess 
(the  spherical  excess  in  seconds  of  arc  is  equal  approxi- 
mately to  the  area  in  square  miles  divided  by  78);  (2)  the 
computed  length  of  any  side  when  obtained  from  any  other 
side  through  two  independent  sets  of  triangles  is  the  same 
in  both  cases. 

When  the  angles  of  a  quadrilateral  have  been  measured, 
errors  are  certain  to  be  present  and  the  corrections  that 
satisfy  one  of  these  conditions  will  not  satisfy  the  other. 
The  most  probable  values  of  the  corrections  to  the  angles 
are  then  determined  by  the  Theory  of  Least  Squares. 

TESTS  OF  PRECISION. 

Practical  Tests  — In  careful  surveying  where  blunders 
are  eliminated  and  the  systematic  and  accidental  errors  are 
small  and  under  control,  it  is  found  that  the  magnitude  of 
the  errors  increases  in  close  accord  with  the  foregoing 
rational  basis,  that  is,  as  the  square  root  of  the  number  of 
observations.  The  following  practical  tests  of  precision  are 
based  on  this  truth.  (The  diagrams  have  been  prepared 
with  a  view  to  supply  extra  copies  for  insertion  in  the  field 
note  book  where  they  may  be  consulted  as  the  results  are 
obtained.) 

Linear  Errors. — Cumulative  or  systematic  errors  usually 
increase  directly  as  the  length  of  the  line  chained,  while  com- 
pensating or  accidental  errors  vary  about  as  the  square  root 
of  the  length.  AVhile  both  kinds  of  errors  affect  all  linear 
measurements,  the  former  chiefly  control  the  results  of  crude 
and  the  latter  of  accurate  chaining.  It  is  thus  fairly  con- 
sistent to  express  the  precision  of  chaining  in  crude  work 


204  ERRORS  OF  SURVEYING. 

in  terms  of  the  simple  ratio  of  the  length;  but  as  the  chain- 
ing becomes  more  and  more  exact,  the  variation  of  the  dif- 
ferences between  duplicate  measurements  approximates 
more  and  more  closely  to  the  law  of  square  roots. 

Coefficients  of  precision  derived  from  the  latter  relation 
may  be  based  on  either  100-foot  units  or  foot  units  in  the 
distance  chained,  as  preferred.  The  former  basis  is  used  in 
the  chaining  diagram,  while  the  latter  is  found  in  the  last 
paragraph  of  the  explanatory  matter  on  the  second  page 
referring  to  the  precision  of  traverse  surveys. 

The  diagram  of  chaining  errors  shows  chaining  ratios  by 
right  lines  radiating  from  the  origin,  and  the  law  of  square 
roots  by  means  of  parabolas.  The  coefficient  of  precision 
for  a  given  observed  difference  between  duplicate  chainings 
is  determined  by  inspection  from  the  diagram,  interpolating 
between  curves  if  an  additional  decimal  place  is  desired  in 
the  result.  In  actual  practice  a  pair  of  careful  chainmen 
may  determine  the  coefficient  corresponding  to  a  given 
degree  of  care,  and  then  use  this  value  either  in  testing 
their  duplicate  results,  or  in  estimating  the  probable  uncer- 
tainty of  the  lengths  chained. 

For  accurate  chaining  with  the  steel  tape,  duplicate 
measurements  reduced  for  temperature,  etc.,  or  made  under 
sensibly  identical  conditions,  should  not  differ  more  than 
0.05  foot  into  the  square  root  of  the  distance  in  100-foot 
units.  Careful  work  with  the  common  chain  (estimating 
fractions  to  0.01  foot)  should  not  differ  more  than  0.1  foot 
into  the  square  root  of  the  distance  in  100-foot  units. 

A.ngular  Errors. — In  measuring  deflection  angles  by  alti- 
tude reversals,  as  in  railroad  traversing,  there  is,  of  course, 
a  cumulative  discrepancy  due  to  the  collimation  error; 
but  generally  speaking,  careful  angular  measurements  with 
good  instiuments  are  subject  only  to  compensating  or  ac- 
cidental errors.  Under  the  latter  conditions  the  magnitude 
of  the  error  of  closure  in  a  series  of  angles,  either  in  a 
closed  polygon  or  about  a  point,  varies  about  as  the  square 
root  of  the  number  of  angles.  This  relation  is  indicated 
graphically  in  the  diagram  of  angular  errors. 

In  measuring  angles  with  a  transit  reading  to  the  nearest 
minute,  the  compensating  uncertainty  of  a  single  reading 
is  probably  somewhat  under  0. 5  minute  per  angle,  or  about 
one  minute  for  the  closure  of  a  triangle.  If  a  reading  glass 


TESTS  OF  PRECISION.  205 

THE  PRECISION   OF  CHAINING. 


THE  PRECISION  OF  ANGULAR  MEASUREMENTS. 

;s 


0  5  10  IS 

Number    of   Angles  in  Polygon   or  Series,*. 


THE   PRECISION    OF    TRAVERSE    SURVEYS. 

The  error  of  closure  of  a  traverse  is  usually  expressed   as   the 
ratio  of  the  calculated  linear  error  to  the  length  of  the  perimeter  of  the 
fie/at  or  polygon.      The  following  table  shows    the  limits   prescribed   by 
various    authorities 

Prescribed    Limits  For    Closure   Of  Traverses. 


Authority. 

Conditions. 

L'im'its. 

Cillespfe.  (1855). 

"Surveying"  p.  /49. 

Compass    Surveys 

I.-3OO    to  I:IOOO 

Alsop.  f/8S7J. 

Compass  Surveys. 

I:  SOO 

"Surveying"  p.  199. 

Transif  Surveys. 

1:1000   to  /:isoo 

Davies.  (/87O). 

"Surveying*  p.  127. 

farm  Surveys. 

/:soo   to  i:/ooo 

Jordan.  (1877). 

German  Gov't  Surveys. 

"Handbuch  der 

Baden  Instructions. 

i:4OO 

Yermessungs- 
ffun  de"  Vot.  /,  p.  £96. 

Str/SS  Gov't  Surveys. 

1.333     to   I-.IOOO 

Ordinary    Country. 

1:400  to  /:8OO 

Mountainous   Country. 

i:Z67  to  1:  533 

Hodgman.  (/88S). 

"Surveying"  p.  119. 

Compass  Surveys. 

/:joo  to  1:1000 

Johnson.  f/886J. 

Farm  Surveys. 

1:300 

"Sur  veying"  p.  SOI. 

City  Surveys. 

I.-/OOO    to  l:5OOO 

Ba/fer.  *  (/88S). 

"Engineers  '  <5ur  veyi  ng 

ins  ti-umen  ts,"  p.  5-3. 

(See  Footnote). 

(See  Footnote). 

Car  hart.  (/888). 

"Surveying"  p.  I6/. 

Ordinary  Farm  Surveys. 

r.SOO 

Leve/  Ground. 

/:/ooo 

Rough  Ground. 

1:200    to  i:3oo 

Average  Transit"  -Surveys. 

1:1200 

Wood. 

(See  Footnote). 

(See  Footnote). 

(Roanoke,  va.,  1892). 
(Baltimore,  Md-,  /894). 

^Precise  Traverses    with\ 
\     Repeated  Angles.            J 

t:/o  ooo 
/:/500o-t-.04frt. 

Raymond.  C/896J. 

"Surveying,"  p.  144. 

Ordinary  Farm  Surveys. 

i:foo 

Good  Farm  Surveys. 

1:2000 

* Baker  derives  the  formula     £.=  p~f  dl  +  72 
£  is  the  permissible  linear  error   of  closure,   P  the  length  of  the 
perimeter,     I'-d  the   ratio   of  the  chaining   error,  and  a   the  angular 
error  of  closure  in  minutes.    A  thorough  test  of  this  formula  under 
a  wide  range  of  conditions  proves  it   to   be  trustworthy. 

However,   the   use  of  a  chaining  ratio,  r.d,  presumably  of  fixed 
value  for  the  same  chainmen,  does  not  accord  with  the  results    of 
experience  in  careful  worK;     for  it  !s    found   that  the  differences 
between  duplicate  chalnings   vary  about  as    the.  square  ryot  of   the 
length  of  Jine. 

On  the  following  pigs   a   simplified  formula  js    obtained  by  as- 
suming the  more  consistent   relation  Just  stated  -for  the  chaining 
errors.      The   results  ars  about  th&  same  as  those  obtained  with 
Baker's  formula^    and  the  form  of  the  expression  is    identical 
Hrith    that  used  by  Wood  in  the    Bo/frmore  Survey.  , 


THE   PRECISION    OF    TRAVERSE    SURVEYS. 

The  reasonable    or  permissible  error   of  closure   of  a  traverse 
survey  may  be  determined   by  the   formula   dorived  be/o*vf  provided 
the  errors  of  ff'eld  iworh  are  under  control  and  their  magnitude 
is  kno*n,  at  /ea-s*  appro* 'fmafely. 
Let  P  =  length  of  perimeter. 

L  -  calculated  error  of  /atftud&s. 

D  — calculated  err-or  of  departures. 

Ea~  actt/a/  or  ca/cu/ared  linear  error  of  c/osure   of  traverse. 

c  —  coefficient  of  precis/on  of  cha/n/'/yg. 


£?=  angular  error  of  c/osure  /n  f-rj/ntjfes. 

ft  =*•  /inear   error  of  c/o-sur^  afc/€t  ro  angu/ar  errors. 

Ep= perrnissib/e.or  reasonable  //'near  error  of  clo$ure>  due  to 

errors  of  chaining  and  angle. 

/n  the  triang/e  of  error    the  hypothenuse    /$      £^^fLz-rDz. 
/n   Diagram  A  be/ow   va/ttes  of£a  may  be  read  c/o&e  enough   for 
most    coses.      Diagram  A  rhay  a/so  serve  a-s  a  crude  graph/ oaf  *rraY- 
erse   tab/e,    and  b/tmders    in  fhe   fie/a"  i/yorM  may  &e  focated  toy  /'r. 

/n  carefa/  chaining  by  men  of  some  training,  the  error*  rar/e>$  abasi- 
as the  square  root  of  the  d/'stance.  /f*c  be  the  compensating  error- 
for  the  unit  distance,  then  C=  cVr>. 

arrrcng  the  sia'es  in  proportion  to  their  lengths.    Assuming  rhis  to  b& 
the  case,  the  resufting  linear  error  /$  A-aP.arc/'^  .OOOSaP. 

In  cjooa4  worK  -the  errors  are  &fr>a/f  in  amount  and  eauaf/y 
liable  to  6e  p/us  and  minus.       Hence,     the  pro&ab/e  error  of  c/osxr-c- 
due  to  the  t*o  causes,  i.e.   rhe-  reasonab/e  or  perm/'-S&iMe  //'near-  e-r~ 
ror  of  c/osure   /s    Ep  =  ^A*+C*  =JtO0O3ctP)*+c*P  - 

7~h/s  forma/a  may  be  much  'Simplified'  by  comp/etfna,   trt&  sat/ar^ 
anct  dropping   the  negative    ferm  under  the   rad/'cu/,    whence   with 
sufficient  exactness,    there  results  the  qeneraJ  formu/ct 
Ep=.0003af>+l7OOc* (I) 

77?^  very  exact  sfandard,  P-Z-/5 OOO+.O4-ft.,  used  at  Baltimore, 
(see  table,  precea'ing  page),  may  be  obtn/'n&el  from  (t}  by  matting  aj 
•somewhat  /ess  that 


may  be  obtat/'n&el  from  (t}  by  maHing  aj 
?ufe,  and  c  =  .oo5rf.,  these  vafaes  bring 


ay  be   taHen  as  fo//otvs:-  For  best  w 
ige   work    (c<,.O!Oft.),.Zft.;   for   fa 


The    ya/ue   of  c  may  be 
the    chaining  term   of  (I) 

worH  (c<.OiS)r  .4* ft.;  ana"  for  poor  worn  (c^-020),  .8ft.     /n  &are- 
ful  traverse  surveys  the  angle  ftrrm  alone  afFords  a  rigid  test,   so  that 

for  the   genera/  ru 


A.  Actual  Error. 

10'  15°  Z0°  Z5°  50°    35°  40° 


B.  Permissible  Error. 

See    Formula    CZ). 


THE    PRECISION    OF    LEVEL    CIRCUITS.  - 

The  precision  of  spirit  leveling  is  expressed    by   the  formula 
Error  of  Closure  =  Constant  1 'Length  of  Circuit. 

In  the  following  summary  of  practice  in  representative  Surveys  of 
The  United  Starts,  £  is  the  maximum  limit  of  error  of  closure  of  a 
tevel  circuit  having  a  length  of  K  kilometers  or  M  miles. 

MAXIMUM  PERMISSIBLE  ERROR  OF  CLOSURE. 

Metric  UniT&  British    Units. 

NAME  OF  SURVEY.  Coefficient  TO  Coefficient  to  nearest 

nearest   mm.  O.OOIft.         001  ft. 

Chicago  Sanitary  District.  E  =  3mmtfT  =  0. 012  ft.^M      =  O.OIft.iM 

Missouri  River  Commission.  £  =  3mmVSK  =  0.018  ft.  Y^F] 

Mississippi  River  Commission.  (1891).     E=  3mmffi<  =  0.0/8  ft.  W  ^=  0.02  ft.iM 
Mississippi  River  Com'n (Before  1891).  E-  5mmrfrT =  0.021  ft.^W) 
United  States  Coast  Survey.  E=  SmmjIzR  -  0.029  ft.  ~/M     -  0.<75  ft.^M 

United  States  Lake  Surrey.  E=IOmmlfK  =  0.042  ft.  W    =0.04ft.iM 

Umted  States  Geological  Survey.      E=  0.050  ft.  VM'   =O.Q5ft.^M 

A  simple  practical  test  of  the  dearee  of  precision  attained  in  spirit 
leveling  is  found  in  the  last  column  Of  the  above  table.  This  graduated 
scale  of  precision  is  aiven  below  gi-aphically  for  distances  to  ten  miles. 


000 


Length 


234 

of  Level    Circuit,  Af,  Miles. 


THE   PRECISION    OF^  LEVEL    CIRCUITS. 
(For  Good  Average  Practice.) 

When  the  length  of  tht  level  circuit  is  /fnotvn  in  100-ft  stations, 
or  rthen  merely  the  number  of  settings  of  the  instrument   and  the  approx- 
imate average   distance    covered  per  setting  are   known,    the  following 
modifications  of  the  preceding  test  are  valuable. 

Let  £=  maximum  permissible   error  of  closure  of  level  circuit. 
M  =  length  of  level  circuit  in  miles. 
L  =  ,         ,.   100-ft.  stations. 

L'=  approximate    average  distance  covered  per  setting 

of  the  instrument  in  100-ft.  stations. 
5  =  number  of  instrumental  seltings  in  the  circuit. 

For  good  average    work    with  the  engineers'  level 


O.OO7ftrfL 


and 

Substituting   for   400  -ft  average  sights,  L'=8,  E  =  0.0135ft.  VJ 

-  3  SO--         •  ••        L'=7,  E  =0.0/82  ft.  T/J 
••      3  00--         ~              •        L'=6,  E=O.OI63ft.TfS 

•  250-         "  "        L'=S,  E=  0.0154  ft.VJ 
For  a  very  rapid  approximate   check  under  ordinary  conditions,  it  may 
be  assumed   that    E  —  O.OZft.YS^.        A  graphical  representation  of  these 
formulas   is  given  below. 

Length   of  Level   Circuit,    M,  Miles. 
0  S  10  15         20 


E5 


30 


35 


40 


AS 


0.35 


'0.00 


0  10          20          30          40          50          60          70  80  90          100 

Length  of   Level   Circuit,  L.  100-Foot  Stations;    or  Number  of   Level  Settings,  5. 


210  ERRORS  OF  SURVEYING. 

be  used  and  the  vernier  reads  to  the  nearest  half  minute, 
the  uncertainty  is  still  further  reduced. 

Again,  in  estimating  the  needle  reading  of  a  compass  to 
the  nearest  5  minutes  (one-sixth  part  of  half-degree),  the 
uncertainty  of  reading  alone  is  perhaps  8  minutes,  although 
this  is  increased  by  other  conditions  such  as  sluggishness 
of  needle,  etc.,  probably  causing  an  uncertainty  of  as  much 
as  5  minutes  per  angle,  which  latter  limit  would  produce  an 
error  of  closure  of  a  triangle  of  say  10  minutes,  and  of  a 
five-sided  polygon  of  perhaps  the  same  amount.  ^See  dia- 
gram.) 

Traversing  Errors. — The  errors  of  traversing  are  made 
uj)  of  the  combined  errors  of  linear  and  angular  measure- 
ments. If  the  error  of  closure  as  determined  from  the  lati- 
tudes and  departures  is  large,  the  work  should  be  scanned 
closely  to  detect  blunders  such  as  the  substitution  of  sine 
for  cosine,  errors  of  100  feet  in  chaining,  misplacing  deci- 
mal point,  etc.  After  establishing  the  consistency  of  the 
residual  errors,  they  should  be  distributed  either  -in  propor- 
tion to  the  lengths  of  the  several  courses,  as  in  the  more 
common  usage,  or  in  the  proportion  of  the  respective  lati- 
tudes and  departures,  as  would  seem  to  be  more  consistent. 
If  the  several  courses  have  not  been  surveyed  with  like 
precision,  weights  should  be  assigned  in  distributing  the 
errors.  Absurd  refinements  should  be  avoided  in  making 
the  distribution  of  errors. 

Leveling  Errors. — Perhaps  in  no  phase  of  surveying 
measurements  is  it  more  clearly  established  that  accidental 
errors  follow  the  law  of  square  roots  than  in  careful  leveling. 
The  precision  diagrams  are  based  on  best  current  usage. 


CHAPTER  X. 
METHODS  OF  COMPUTING. 


Introduction. — To  no  one  is  the  ability  to  make  calcula- 
tions accurately  and  rapidly  of  more  value  than  to  the  engi- 
neer. Many  fail  to  appreciate  the  value  of  rapid  methods 
of  calculation,  and  have  no  conception  of  the  amount  of 
time  that  can  be  saved  by  the  skillful  use  of  arithmetic, 
logarithms,  reckoning  tables  and  computing  machines. 

In  the  Held  the  engineer  has  to  depend  upon  the  ordinary 
methods  of  arithmetic,  or  a  table  of  logarithms  for  his 
results.  The  use  of  these  aids  should  therefore  receive  special 
attention,  for  the  engineer  cannot  afford  to  lose  the  time  of 
his  assistants  while  he  makes  unnecessary  or  extended  com- 
putations. 

In  the  office  tables  of  squares,  reckoning  tables,  slide  rules 
and  computing  machines  can  be  used  in  many  cases  with 
profit. 

Consistent  Accuracy. — It  is  safe  to  say  that  at  least  one- 
third  of  the  time  expended  in  making  computations  is 
wasted  in  trying  to  attain  a  higher  degree  of  precision  than 
the  nature  of  the  work  requires. 

In  making  arithmetical  computations  where  decimals  are 
involved  it  is  a  common  practice  to  carry  the  result  out  to 
its  farthest  limit  and  then  drop  a  few  figures  at  random. 

In  using  logarithms  time  and  labor  are  lost  by  using 
tables  that  are  more  extensive  than  the  data  will  warrant. 
The  relative  amount  of  work  in  using  four,  rive,  six  and 
seven-place  tables  is  about  as  1,  2,  3  and  4.  Besides  the 
extra  labor  involved,  the  computer  has  a  result  that  is  liable 
to  give  him  an  erroneous  idea  of  the  accuracy  of  his  work. 

In  making  computations,  in  general,  calculate  the  result 
to  one  more  place  than  it  is  desired  to  retain. 

If  several  numbers  are  multiplied  or  divided,  a  given 
percentage  of  error  in  any"  one  of  them  will  produce  the 
same  per  cent  of  error  in  the  result. 

In  taking  the  mean  of  a  series  of  quantities  it  is  consist- 
ent to  retain  one  mpre_ptace  than  is  retained  in  the  quan- 
tities themselves. 


212  METHODS  OF  COMPUTING. 

In  direct  multiplication  or  division  retain  four  places  of 
significant  figures  in  every  factor  for  an  accuracy  of  about 
one  per  cent.;  retain  five  places  of  significant  figures  in 
every  factor  for  an  accuracy  of  about  one-tenth  of  one  per 
cent. 

I  ,OG ARITHMIC  CALCULATIONS. 

Logarithm  Tables.— Logarithm  tables  contain  the  decimal 
part  of  the  logarithm  called  the  mantissa,  the  integral  part 
called  the  characteristic  is  supplied  by  the  computer. 

Four-place  tables  give  the  mantissa  to  four  decimal 
places  of  numbers  from  1  to  999,  and  by  interpolation  give 
the  mantissa  of  numbers  from  1  to  9,999.  Four-place  log- 
arithms should  be  used  where  four  significant  figures  are  suf- 
ficient, and  should  not  be  used  where  an  accuracy  greater 
than  one-half  of  one  per  cent  is  required. 

Five-place  tables  give  the  mantissa  to  five  decimal  places 
of  numbers  from  1  to  9,999,  and  by  interpolation  give  the 
mantissa  of  numbers  from  1  to  99,999.  Five-place  loga- 
rithms should  be  used  where  five  significant  figures  are 
sufficient,  and  should  not  be  used  where  an  accuracy  greater 
than  one-twentieth  of  one  per  cent,  is  required.  Five-place 
tables  are  sufficiently  accurate  for  most  engineering  work. 

Six-place  tables  give  the  mantissa  to  six  decimal  places 
of  numbers  from  1  to  9,999,  and  by  interpolation  give  the 
mantissa  of  numbers  from  1  to  99,999,  the  same  as  the  five- 
place  tables.  Six-place  tables  are  of  no  practical  value  as 
the  labor  of  using  a  six  instead  of  a  five-place  table  is 
about  as  2  to  3,  and  as  the  interpolation  for  the  next  signif - 
cant  figure  is  made  with  larger  differences:  it  is  less  reli- 
able than  with  the  five-place  table. 

Seven-place  tables  give  the  mantissa  to  seven  decimal 
places  of  numbers  from  1  to  99,999,  and  by  interpolation 
of  numbers  from  1  to  999,999.  Seven-place  tables  are 
rarely  needed  in  engineering  work,  except  in  triangulation 
work  where  the  angles  are  measured  by  repetition. 

ARITHMETICAL  CALCULATIONS. 

Requirements. — To  become  a  rapid  computer  the  follow- 
ing requirements  are  essential: 

(1)  A  good  memory  for  retaining  certain  standard  num- 
bers for  reference. 


ARITHMETICAL  CHECKS.  213 

(2)     The  power  of  performing  the  ordinary  simple  arith- 
metical operations  of  multiplication,  division,  etc.,  on  num- 
bers with  facility,  quickness  and  accuracy. 
.    (3)     The  power  of  registration,  /.  e.,  of  keeping  a  string 
of  numbers  in  the  mind  and  working  accurately  upon  them. 

(4)  The  power  of  devising  instantly  the  best  method  of 
performing  a  complicated  problem  as  regards  facility, 
quickness  and  certainty. 

It  is  obvious  that  all  do  not  have  the  ability  to  become 
rapid  computers,  but  even  these  can  become  fairly  skillful 
by  constant  practice  and  perseverance.  The  ordinary  pro- 
cesses of  arithmetic  should  be  performed  with  numbers  in 
all  possible  positions.  No  more  figures  should  be  put  down 
than  necessary,  and  all  operations  should  be  performed 
mentally  whenever  possible.  In  the  mental  part  the  results 
should  alone  be  stated,  much  time  being  lost  by  repeating 
each  separate  figure. 

Checks. — In  order  to  check  his  work  the  computer  should 
keep  the  following  well  known  properties  of  numbers  well 
fixed  in  his  mind: 

(1)  The  sum  or  difference  of  two  even  or   of  two   odd 
numbers  is  even . 

(2)  The  sum  or  difference  of  an  even  and  odd  number  is 
odd. 

(3)  The  product  of  two  even  numbers  is  even. 

(4)  The  product  of  two  odd  numbers  is  odd. 

(5)  The  product  of  an  even  number  and  an  odd  number 
is  even. 

(6)  Checking  results  by  the  familiar  operation  of  cast- 
ing out  the  9's  depends  upon  the  following  properties  of 
numbers: 

(a)  A  number  divided  by  9  leaves  the  same  remainder 
as  the  sum  of  the  digits  divided  by  9.     For  example: 

4384^9=487+1 

(4+3+8+4)^-9=2+1 

(b)  The  excess  of  9's  in  the  product  equals  the  excess  of 
9's  in  the  product  of  the  excesses  of  the  factors. 

473,295   Excess  =  3 
4,235   Excess  =  5 


2,004,404,325   Excess 


[5 


214  METHODS  OF  COMPUTING. 

(r)  The  excess  of  9's  in  the  dividend  equals  the  excess 
of  9's  in  the  product  of  the  excesses  in  the  divisor  and  quo- 
tient plus  the  excess  in  the  remainder: 

56/244:}  Excess  in  divisor     =  2 

4:{+:{5     Excess  in  quotient  =  7 
Excess  in  remainder=8 
Excess  in  (2X74- 8) =4  / 
Excess  in  dividend  =  4  \    ] 

(7)  Results  should  be  checked  by  taking  aliquot  parts 
wherever  possible,  and  by  performing  the  operations  in 
inverse  order  or  performing  inverse  operations,  Computa- 
tions performed  by  means  of  logarithms  should  be  checked 
by  making  the  computations  roughly  by  means  of  arithme- 
tic. The  probability  of  error  should  be  recognized  and  pre- 
caution taken  to  verify  results. 

ADDITION. — Since  the  eye  is  accustomed  to  pass  from  left 
to  right  time  can  be  saved,  where  the  columns  are  not  too 
long,  by  adding  in  the  same  way.  The  device  of  increasing 
or  diminishing  the  numbers  to  make  them  multiples  of  ten 
and  then  subtracting  or  adding  to  the  result  is  very  con- 
venient, especially  where  several  columns  are  added  at  one 
time. 

A'.r.  /.—  96 

47     143 
212     69 
32 

87    331 
49 

380 

The  mental  work  in  detail  is  as  follows: 
100+47=147;    147—4=143;    143+70=213;   213—1  =  212: 
212+30+90=  332 ;  332- 1  =  33 1 ;  331+50    38 1 ;  38 1  - 1 = 380 

Expert  accountants  use  the  method  of  adding  col- 
umns in  groups  of  10,  20,  30,  etc..  -small  figures,  indicat- 
ing the  number  of  the  group,  being  placed  along  the  column 
at  intervals  depending  upon  the  computer.  This  method  is 
well  adapted  to  the  addition  of  long  columns  where  one  is 
liable  to  be  called  away  from  his  work.  The  progress  of 
the  work  being  then  shown  by  the  number  of  the  group 
plus  the  excess. 


K.r.  7.— 4,324X  625  =  4,324(5X.1QJ )      (4,324,OOOX  5) 


MULTIPLICATION.  215. 

MULTIPLICATION.— In  order  to  make  the  best  use  of 
the  methods  given,  the  computer  should  have  perfect  com- 
mand of  the  multiplication  table  as  far  as  20  at  least. 

Multiples  of  10. — To  multiply  by  some  number  which  is 
a  factor  of  10  or  some  multiple  of  10,  for  example:  Multiply 

A  bv  B,  where  B=  — 
d 

Annex  n  ciphers  to  A,  multiply  by  C  and  divide  by  d. 

2,702,500. 

/vr.  j?._ 7,924X25     792,400  s-4     198,100. 

Squaring  Small  Numbers. — Numbers  may  "be  squared 
mentally  by  the  following  rule:  Add  to  or  subtract  from 
one  factor  enough  to  make  its  units  figure  zero.  Subtract 
from  or  add  to  the  other  factor  the  same  amount.  Multiply 
together  this  sum  and  difference,  and  to  the  product  add 
the  square  of  the  amount  by  which  the  factors  were  increased 
or  diminished. 

Proof.-—  a2  —  b2  =  (a+b)  (a— b) 

a2     (a+b)(a— b)+b2 
(76) 2     (72x80i+42     5.776 
(127)3     (124X130)4-33     16,129 
Kx.  3.—         (64)2     (6X6|)+(i):'     39-!1,,1 
K.c.  4.—         (6.1) 2  .  (6X7)  + (|)2     42} 
Ex.  '>.—        (7.5)2     (7X8)+(5)2     56.25 

It  will  be  seen  that  the  process  is  very  simple  where  the 
units  place  is  5. 

(2)  When  the  tens  differ  by  unity  and  the  sum  of  the  units 
equals  10.  numbers  may  be  multiplied  by  the  following  rule: 
From  the  squares  of  the  tens  of  the  larger  number  subtract 
the  square  of  the  units  of  the  larger  number.  For  the  num- 
bers may  be  represented  by  (a+b)  and  (a— b),  and  the 
product  will  be  (a+b)(a— b)'  a2— b2. 

K,r,  6'.— (93X87)  =  903— 32  =  8,100  — 9  =  8,091. 


216  METHODS  OF  COMPUTING. 

(3)  The  product  of  composite  numbers  is  best  obtained 
mentally  by  resolving  them  into  their  factors  and  taking 
the  products  of  the  factors. 

26X 36    -9X13X 8   -=936 
48X24   <24)2X2   .-1,152 

(4)  Having  the  square  of  any  number  the  square  of  the 
number  next  higher  is  obtained  by  the  following  rule:     To 
the  known  square  add  the  number  and  the  next  higher  and 
the  result  will  be  the  square  of  the  next  higher  number. 

Ex.9.—    (25)2     625.     (26) 2-  -625 +25+26     676 

(5)  A  very  close  approximation  to  the  square  of  a  quan- 
tity which  is  very  near  unity  is  obtained  by  adding  algebra- 
ically two  times  the  difference  between  the  quantity  and 
unity  to  the  quantity. 

Proof.  —  (lib)2     I±2b-f-b2  =  l±2b,  (approximate). 
Ex.  10.—  (1.05)2=  1+2  (1.05— !)  =  !+.  10=1. 10 
Ex.  11. -(.94)2=1—  2  (1— .94)=!— .12=. 88 
Ex.  12.— (2.034)  2=22(1+2X.017)=4(1.034)=4. 136 

Cross-Multiplication. — This  consists  in  aking  the 
product  of  each  digit  in  the  multiplicand  by  each  digit 
in  the  multiplier  and  taking  the  sums,  products  of  the  same 
denomination  being  determined  thus:  unitsX  units  gives 
units;  tensX units  and  unitsXtens  gives  tens;  unitsX 
hundreds,  tensXtens  and  hundredsX  units  give  hundreds, 
etc.  All  products  are  added  mentally,  only  the  final  result 
being  put  down. 

Ex.  1.— (2,347)  2=5,508,409  the  final  result  being  all  that 
it  is  necessary  to  write  down.  The  mental  work  is  as 
follows,  the  figures  in  heavy  type  being  figures  in  the  pro- 
duct: 7X7=49;  4  +  2(7X4)=60;  6+2(7X3)+42=64; 
6+2  (2X7)+2(3X4)=58;  5+2  (2X4)+32=30;  3+2(3X2) 
=  15;  l  +  22=5. 

Ex.  2. — The  product  of  any  two  numbers  may  be  found 
in  the  same  manner. 


CROSS-MULTIPLICATION.  217 


The  mental  work  is  as  follows:  8X2=6;  3X3+8X2= 
25;  2+3X4  +  8X3+5X2=48;  4+3x9+8x4+5X3+2X2 
=82;  8+8X9+5X4+2X3=106;  10+5X9+2X4=63;  6+ 
2X9=24. 

Ex.  3.  —  The  process  of  cross-multiplication  may  be  sim- 
plified as  follows:  Required  to  multiply  4,328  by  736; 
write  the  multiplier  on  a  slip  of  paper  in  inverse  order  and 
place  it  below  the  multiplicand  with  the  left  hand  figure 
below  the  units  place  of  the  multiplicand  thus: 


Multiply  together  the  figures  in  the  same  vertical  column, 
6X8=48;  set  down  the  8  and  carry  the  4;  then  move  the  slip 
one  space  to  the  left,  thus, 

4,328 

inn 

8 

Multiplying  together  the  figures  in  the  same  vertical  columns 
and  taking  the  sum,  4+6X2+3X8=40;  set  down  the  0  and 
carry  the  4;  then  move  the  slip  one  space  to  the  left, 
multiplying  together  the  figures  in  the  same  vertical  col- 
umns, adding,  etc.,  we  will  finally  have  the  work  standing 
thus  : 


liemo\  ing  the  slip  we  have 

4,328 
736 


3,185,408 


218  METHODS  OF  COMPUTING. 

The  multiplier  may  be  written  on  the  bottom  of  a  sheet 
in  inverse  order  and  placed  above  the  multiplicand  instead 
as  above  described.  The  work,  however,  is  very  much 
simplified  by  simply  writing  the  multiplier  in  inverse  order 
without  using  the  slip: 


The  mental  work  being  as  follows:      6  -  S  -  4s:    4+6x2 
+8x8=40;  4+6X3+2X  3+7X8=84;  8+6X4-:;     •>     7 
2=55;    5  +  3X4+7x3=38:3+7x4=31.       It  \\  ill  he  set-n 
that  this  device  removes  most  of  the  mental  strain,  there 
being  no  cross-products. 

CONTRACTED  MULTIPLICATION.  —  In  multiplying 
decimals,  when  the  product  is  required  to  a  few  places  of 
decimals,  the  work  may  be  shortened  as  follows:  Required 
a  product  correct  to  the  nth  decimal  place.  Write  the  multi- 
plier with  its  figures  in  inverse  order,  its  unit  place  under 
the  nth  decimal  place  of  the  multiplicand.  Multiply  the 
multiplicand  by  the  figures  in  the  multiplier,  beginning 
with  the  ri  ht  hand  figure:  rejecting  those  fiuur  s  in  the 
multiplicand  which  are  to  the  right  of  the  figure  used  as  a 
multiplier,  increasing  each  product  by  as  many  units  as 
would  have  been  carried  from  the  rejected  part  of  th^ 
multiplicand,  taking  the  nearest  unit  in  each  case  place  the 
right  hand  figure  of  each  partial  product  in  the  same  col- 
umn, and  add  as  in  common  multiplication. 

In  most  cases  it  is  best  to  carry  one  more  place  than  re- 
quired. The  following  examples  illustrate  the  process: 

Ex.  1. — The  radius  of  a  circle  is  420.17  ft.  What  is  its 
semicircumference  to  nearest  0.01  ft.?  (V  =  3.14159265  I 

In  the  work  below  the  partial  products  in  the  contracted 
multiplication  are  seen  to  correspond  to  the  partials  of  the 
common  method,  tiken  in  reverse  order,  the  part  to  the 
right  of  the  vertical  line  being  rejected.  The  contracted 
multiplication  is  carried  one  more  place  than  required.  A 
dot  is  placed  above  each  figure  when  it  is  rejected  from  the 
multiplicand. 


CONTRACTED   MULTIPLICATION.  219 


420.17 
3./4/S93 


ffo 


I2605/ 


/320.003  /3Z0.003 


Z605I 
8/53 
08S 
17 


'3081 


Ex.  a.—  The  observed  length  of  a  line  is  2231.63  ft. 
with  a  tape  having  a  length  of  100.018  ft.  Required  the 
reduced  length  of  the  line  to  the  nearest  0.01  ft. 

Noting  that  each  foot  of  the  tape  =  1.00018  ft. 


Z23/.63  2Z3/.63 

&l  OOO.I  /.OOP  /  8 

223/6-3  /7\8S304 

22  ^2\3/63 

/8  223/63\000 


2232.03  B232.03\/6934 

EJ-.  .?._Same   observed   length    with   a  tape   99.()82  ft. 
long.     Required  the  reduced  length. 

Each  foot  of  the  tape  =  0.99982  (=  1—0.00018)  ft. 


223/.6S 
0.99  98  a 


20084 


I'l.f.  4  — To  compare  contracted  multiplication  with 
logarithmic  work,  calculate  861.3  ft.  X  sin  17°  19' to  the 
nearest  0. 1  ft. 


220  METHODS  OF  COMPUTING. 


=  2.408864 


2S6-4 

CONTRACTED  DIVISION.— If  the  quotient  is  desired  cor- 
rect to  the  nth  decimal  place,  the  followitg  method  may  be 
used:  Find  one-half  of  the  desired  figures  in  t^he  quotient 
in  the  usual  way  and  do  not  bring  down  a  figure  for  the 
last  remainder.  Drop  a  figure  from  the  right  of  the  divisor 
and  find  another  figure  in  the  quotient.  Then  without 
bringing  down  any  more  figures  continue  to  discard  figures 
from  the  divisor  until  the  required  places  are  obtained. 

Ex.  1-—  Divide  443.9425  by  24.311  to  nearest  hun- 
dredth. There  will  be  four  figures  in  the  quotient,  so  we 
will  find  the  first  two  in  the  ordinary  way.  A  dot  is  placed 
over  each  figure  in  the  divisor  when  it  is  rejected. 

34.32)  44 3. 9 42S  (t8.2S 


Divisor  Near  Unity. — When  the  divisor  is  near  unity  a 
very  close  approximation  is  given  by  the  method  shown  in 
the  following  problems: 

Ex.  i.—  1  0Q39-4  =5  (l—.003254)=5x. 996746=4. 98373 
correct  to  within  one  unit  in  the  fifth  place. 

Ex.  2.—  -^  =  7  ( 1+  (  1-  .9982))  7X  1.0018-  7.0126 
correct  to  the  last  place. 


SQUARE  ROOT.  221 

CONTRACTED  SQUARE  ROOT.  A  result  correct  to  a  re- 
quired number  of  decimal  places  may  be  found  by  a  process 
similar  to  the  method  employed  for  contracted  division. 

Ex.  /.—Required  the  square  root  of  12,598.87325  correct 
to  thousandths.  We  see  by  inspection  that  the  root  will 
contain  six  h'gures.  Find  in  the  ordinaiy  way  the  first 
three  figures.  Form  a  new  trial  divisor  in'the  usual  way, 
and  bring  down  only  one  figure  for  the  dividend  in  place  of 
two.  Find  the  remaining  figures  by  contracted  division. 


The  last  figure  brought  down  is  not  increased  whatever  it 
may  be  followed  by,  since  the  contracted  process  tends  to 
make  the  result  a  little  too  large.  This  method  may  be  ap- 
plied to  the  extraction  of  cube  roots,  where  it  saves  much 
work  in  finding  long  tiial  divisors. 

Square  Root  of  Small  Numbers  — The  approximate  square 
roots  of  small  Lumbers  may  be  found  by  means  of  the 
following  rule:  Divide  the  given  number  by  the  number 
whose  square  is  nearest  the  given  number.  The  arith- 
metical mean  of  the  quotient  and  divisor  will  be  the  ap- 
proximate square  root  of  the  number.  The  nearer  the  num- 
ber is  to  a  perfect  square  the  less  the  error.  For  example, 

Ex.  1.—  ^35=:  (a/+6)  -4-  2  =  5.92. 
Ea^  2.^  V~%~=  (f  +  3)  -s-  2  =  2.83. 
E.T.  3.  —  V"79=  •(«+'  9)  +  2  —.8.89. 
Ex.  4.—  Vl28— (H-H)-*-2--  11.31. 


222  METHODS  OF  COMPUTING. 

Square  Root  by  Subtraction.  — While  it  possesses  no  points 
of  merit  in  this  connection,  it  would  not  be  proper  to  pass 
the  subject  of  square  root  without  presenting  the  novel  meth- 
od of  extracting  square  roots  used  with  the  Thomas  Com- 
puting machine.  The  method  depends  upon  the  relation 
existing  between  odd  numbers  and  squares  in  the  system  of 
numbers  having  a  radix  ten.  If  we  sum  up  the  odd  num- 
bers, beginning  at  1,  we  will  observe  the  following  relation: 

1--13;  1+3--4---22;  l  +  3+5=9-=3a;  1  +  3+5+7-15  4'-', 
etc.  It  will  be  seen  that  the  square  root  of  the  sum  in  each 
case  is  the  number  of  the  group. 

The  method  of  extracting  square  roots  is  as  follows:  Point 
off  in  periods  of  two  figures  each:  subtract  from  the  left 
hand  period  the  odd  numbers  in  order,  beginning  at  unity, 
until  a  remainder  is  obtained  less  than  the  next  odd  num- 
ber. Write  for  the  first  figure  in  the  root  the  number  which 
represents  the  number  of  subtractions  made.  Double  the 
root  already  found  and  annex  unity.  Subtract  as  before, 
using  for  subtrahends  the  successive  odd  numbers,  the  root 
figure  being  the  number  of  subtractions  made. 

Ex.  1. — Extract  the  square  root  of  53,824. 


3 2  subtract  ons 


MISCELLANEOUS  FORMULAS'.— The  engineer  should 
have  ready  knowledge  concerning  approximate  formulas  and 
values.  This  knowledge  can  be  obtained  by  the  expenditure 
of  very  little  energy  and  time  if  rightly  applied.  For  ready 


COMPUTING  INSTRUMENTS. 


223 


~t 


224  METHODS  OF  COMPUTING. 

computation  and  reference  he  should  reduce  as  much  of 
his  knowledge  as  possible  to  mathematical  language  and 
express  known  relations  by  means  of  formulas.  The  fol- 
lowing will  illustrate  this  point. 

Cost  of  Sewer  Pipe.— The  Western  Price  List  of  sewer 
pipe  is  comprised  in  the  formula,  C-=0.4  d2+14.  Where 
C-=cost  in  cents  per  foot  and  d—  diameter  of  pipe  in  inches 
For  75  per  cent  off,  the  formula  is  C1  0.1  da+3.5,  a  form- 
ula very  easily  remembered. 

RECKONING  TABLES.— Tables  for  use  in  computing  are 
so  numerous  and  well  known  that  it  would  be  useless  to  trj' 
to  refer  to  them  by  name.  Two  valuable  tables  for  obtain  - 
ing  products  of  numbers — which  are  well  known  in  Ger- 
many, but  comparatively  unknown  in  this  country — are, 
"Crelle's  Rechentafeln,"  which  gives  the  products  of  num- 
bers of  three  significant  figures  by  three  significant  figures  to 
999  by  999;  and  "Zimmerman's  Rechentafeln,"  which  gives 
the  products  of  numbers  of  two  places  of  signigcant  figures 
by  numbers  of  three  significant  figures  to  100  by  999. 

COMPUTING  MACHINES.— In  Fig. 40,  (a)  is  a  Kuttner 
reckoning  machine;  (b">  a  Thomas  computing  machine;  (c)  a 
Fuller  slide  rule;  (d)  a  Thacher  slide  rule;  (e)  an  ordinary 
slide  rule;  (f)  a  Colby  Stadia  slide  rule;  (g)  a  Colby  sewer 
slide  rule;  (h)  a  Grant  calculating  machine;  (i)  a  full  circle 
protractor;  (j)  a  Crozet  protractor;  (k)  a  protractor  tee 
square;  (1)  a  polar  planimeter;  (m)  a  "jack  knife"  planim- 
eter;  (n)  a  pantagraph;  (o)  a  section  liner;  (p)  a  spher- 
ical planimeter. 

In  using  the  "jack  knife"  planimeter,  the  point  is  placed 
at  the  center  of  gravity,  and  the  knife  edge  is  placed  on  a 
line  passing  through  the  center  of  gravity  of  the  figure. 
The  point  is  then  made  to  traverse  the  perimeter  of  the  fig- 
ure to  be  measured;  passing  out  to  the  perimeter  and  re- 
turning to  the  center  of  gravity  of  the  figure  on  the  same 
line.  The  distance  from  the  final  position  of  the  knife  edge 
to  the  line  through  the  center  of  gravity,  multiplied  by  the 
length  of  the  arm  of  the  planimeter  will  give  the  area  of 
the  figure.  The  arm  of  the  protractor  is  usually  made  ten 
inches  long  and  the  distance  measured  in  inches. 

The  other  machines  are  described  in  the  instructions  ac- 
companying them  when  purchased. 


CHAPTER  XI. 
FREEHAND  LETTERING. 


Practice  Plates. — A  magnified  scale  is  used  in  the  first  six 
plates  to  give  familiarity  with  form  of  letter  and  numeral, 
and  also  to  produce  freedom  of  hand  motion.  The  six 
plates  should  first  be  made  with  a  soft  pencil  sharpened  to 
a  needle  point,  and  afterwards  with  pen  and  India  ink.  In 
Plate  7  the  height  of  letter  is  that  prescribed  in  Chapter  I. 
This  standard  size  is  not  only  well  adapted  to  field  notes 
and  general  drafting,  but  is  economical  of  execution,  as 
shown  by  the  diagram. 

ECONOMY    DIAGRAM 

ENGINEERING   NEWS  STYLE  OF 

FREEHAND    LETTERING. 


3         4          5          6          7  89          10 

Height  of  Letter   SOths  Inch,  as  per  Samples. 


FREEHAND  LETTERING. 


PLATES. 


227 


228 


FREEHAND  LETTERING. 


^ 

i 


PLATES. 


229 


230  FREEHAND   LETTERING. 


PLATES. 


231 


232 


FREEHAND   LETTERING. 


I 


( 


I 


uv 

J 


